
QassZ|3iZ/XA 
Book L„Si^ 



1 n^ !.-<? 



I / 



\\ 



\ 



( 



/lA^AA r '^- 



Digitized by the Internet Archive 
in 2011 with funding from 
The library of Congress 



http://www.archive.org/details/logicinductivede01jone 







'.r^l 



#■"^4 »^ J^ J 






/^<P<) 



/ 




1 

s 



/^r 



/ 



2r3i 



I 



To 

L. Si M. 



If /6 33 



PREFACE 

This book is intended as a text-book and not at all 
as a contribution to logical theory. It aims to present 
an outline of scientific method as briefly and as con- 
cretely as possible. It is not designed to serve as an 
introduction to general philosophy. Its chief claim to 
novelty is in the arrangement of the subject matter. 
The traditional arrangement in which the deductive 
processes are presented first usually leaves with the 
student the impression that method is chiefly deduction, 
and that there is no very close connection between this 
and the rest of subject. The arrangement, which is 
here adopted, was selected on pedagogical grounds and 
not in the interests of any epistemological theory. 

The justification for dogmatic statements on dis- 
puted points is also pedagogical. Argument on such 
points in a text-book usually fails to interest the stu- 
dent and often tends to make him think that the whole 
subject is in an uncertain state and mostly a matter of 
opinion. Some subjects are treated much more briefly 
than they deserve, but I wished to keep them in due 
proportion with the rest. 

Fallacies are first discussed along with the processes 
with which they are connected, but they are all brought 
together in a later chapter. Many of the exercises are 
new, but I have also drawn freely from other text- 
books. The longer exercises at the end of the book 
give the student an opportunity to bring to bear al- 



vi PREFACE 

most the whole of scientific method, and for this reason 
they seem to me to be very important. 

My indebtedness to Jevons, Hyslop, Mill, and Bow- 
ley will be obvious. I owe much to Aikins' Principles 
of Logic; his broader treatment of many topics and 
his chapters on Testimony, Averages, Statistics, etc., 
were very suggestive. Sidgwick's The Use of Words 
in Reasoning, Creighton's treatment of the Figures 
of the Syllogism in his Introduction to Logic, Hibben's 
use of the idea of system in his Logic and Cramer's 
The Method of Darwin, were also suggestive. I have 
tried to give credit in each case in which I am con- 
scious of having borrowed. 

I am much indebted to three of my former col- 
leagues in Princeton University: to Professor W. T. 
Marvin for going over the whole of the copy and giv- 
ing me much useful advice, and to Professors W. H. 
Sheldon and E. M. Rankin for assistance with the 
proof; and to my colleagues, Professors Woodbridge 
and Montague, for many valuable discussions of 
logical problems. 

A. L. J. 

New York, April, 1909. 



PAGE 



CONTENTS 

PART I 
AN OUTLINE OF SCIENTIFIC METHOD 

Chapter I 

INTRODUCTORY 

Science and Common Sense — Induction and Deduction in- 
cluded in Scientific Method — The Beginning of knowl- 
edge — Natural Sciences and others — The Sources of 
Knowledge, Direct and Indirect — Organizing knowledge 
— Classification as a preliminary step — Language as a 
necessary instrument — Further steps in organized knowl- 
edge — ^What is presupposed? 1 

Chapter II 

FIRST STAGES IN KNOWLEDGE 

Facts and the ways in which they are known — Perception 
and what it includes — Indirect means to knowledge of 
facts , 13 

Chapter III 

CLASSIFICATION 

Types of Classification — Division — Requirements of Classi- 
fication 39 

Chapter IV 
THE USE AND MISUSE OF WORDS 

Discrimination, Conception, Abstraction — Necessity for Lan- 
guage — Terms — Kinds of Terms — Definition — Defects 

of Definitions 45 

vii 



viii CONTENTS 

PAGB 

Chapter V 
PROPOSITIONS 

Kinds of Propositions — Propositions and Terms — The Rela- 
tion of Subject and Predicate — The Distribution of 
Terms in a proposition — Euler's Method — Ambiguous 
Propositions o . . . o 66 

Chapter VI 

INDUCTION 

Generalization and what it includes — Causal Connection — 
Testing Inductive inferences — Complete Enumeration — 
How Generalizations are verified — Observation and An- 
alysis are pre-supposed — Postponing inference till test 
conditions are present — The Inductive Methods. . . 79 

Chapter VII 

VERIFICATION AND DEDUCTION 

Verification and Deduction — Systematic Knowledge — How 
propositions are related to each other — Relations of 
Opposition among propositions which have not identical 
terms — Conversion — Ob version— Contraposition . . , 110 

Chapter VIII 

THE SYLLOGISM 

The Principles of Syllogistic Reasoning — ^The First Figure 
and its Principles — The Second Figure — The Third 
Figure — The Fourth Figure „ . » 126 

Chapter IX 

TRADITIONAL TREATMENT OF THE 

SYLLOGISM 

Traditional treatment — Moods — Figures — Note on the Re- 
duction of the Moods and Figures 137 

Chapter X 

ABBREVIATED AND COMPLEX FORMS OF REASON- 
ING—HYPOTHETICAL AND DISJUNCTIVE 

SYLLOGISMS 

The Enthymeme — Prosyllogisnl and Episyllogism — The So- 
rites — Hypothetical Reasoning — Disjunctive Reasoning 
— More Complex Forms — Extra-syllogistic Reasoning . 151 



CONTENTS ix 

Chapter XI pagq 

I. PROOF AND DISPROOF 11. FAILURE TO PROVE 
Various Kinds of Proof — Failures to Prove — Fallacies . < 166 
General Exercises • . • • . 177 

PART II 
SUPPLEMENTARY METHODS 

Chapter I 

STATISTICS 

Statistics, their uses and limits — Correlation — The Processes 

used in Statistical Investigations 189 

Chapter II 

AVERAGES 

The Arithmetical Average — The " Weighted " Average — The 
Mode — The Median — The Geometrical Average — Meas- 
uring Deviations from an average — Measurement of phe- 
nomena — The Comparison of quantities which cannot be 
measured , 198 

Chapter III 

PROBABILITY 

The Meaning of Probability — Deducing the probability of a 
phenomenon — Dangers to be avoided in interpreting 
probability 213 

Supplement to Part II 

The Graphic Method of Representing Data and Their Re- 
lations 326 

PART III 

THE CONSTRUCTION OF SYSTEMS 

Chapter I 

EXPLANATION 

What is Explanation? 237 



X CONTENTS 

FAGB 

Chapter II 

HYPOTHESIS 

What is an Hypothesis? — The Value of Hypotheses — H6w 
are Hypotheses suggested to us? — Requisites of a good 
hypothesis 246 

Chapter III 

TYPICAL SYSTEMS OF KNOWLEDGE 

The Geometric System — Others closely related to this — Sys- 
tems which are more concerned with concrete phenom- 
ena — Systems of Historical Facts 257 

Exercises in^ the examination of complex reasoning 

Professor James's Argument for his Theory of the*Emotions 
—A. H. Fison on "The Evolution of Double Stars"— 
Huxley on " The Demonstrative Evidence of Evolution " 279 



PART I 
AN OUTLINE OF SCIENTIFIC METHOD 



CHAPTER I 

INTRODUCTORY 

Science and Common Sense. — The methods of sci- 
ence are the methods of all correct thinking. In all 
thinking we are concerned with getting and organiz- 
ing knowledge, or with testing, applying, and devel- 
oping the knowledge we have already acquired. We 
are all aware that correct thinking differs from that 
which is incorrect in its conformity to certain laws. 
These laws are usually spoken of as the laws of 
thought. They are not simply laws of thought, how- 
ever ; they are laws of things as well ; they are the 
laws of the world as we know it. They are adhered 
to, consciously or unconsciously, in all correct think- 
ing, whether casual or systematic. Science differs from 
common sense " only as a veteran differs from a raw 
recruit ; and its methods differ from those of common 
sense only so far as the guardsman's cut and thrust 
differ from the manner in which the savage wields his 
club. The primary power is the same in each case, 
and perhaps the untutored savage has the more brawny 
arm of the two. The real advantage lies in the point 
and polish of the guardsman's weapon ; in the trained 
eye, quick to spy out the weakness of the adversary ; 
in the ready hand, prompt to follow it upon the in- 
slant. But, after all, the sword exercise is only the 
hewing and poking of the clubman developed and 
perfected. 



2 INTRODUCTORY 

" So the vast results obtained by science are won 
... by no mental processes other than those which 
are practised in every one of the humblest and meanest 
affairs of life. A detective policeman discovers a bur- 
glar from the marks made by his shoe, by a mental 
process identical with that by which Cuvier restored 
the extinct animals of Montmartre from the fragments 
of their bones. Nor does the process of induction and 
deduction by which a lady, finding a stain of a peculiar 
color upon her dress, concludes that somebody has up- 
set the inkstand thereon, differ in any way, in kind, 
from that by which Adams and Leverrier discovered a 
new planet. The man of science, in fact, simply uses 
with scrupulous exactness the methods which we all 
habitually and at every moment use carelessly ; and 
the man of business must as much avail himself of the 
scientific method — must be as truly a man of science — 
as the veriest bookworm of us all." ^ 

It is of course true that the conclusions of science 
are often in disagreement with those of common sense, 
but the disagreement is due to the difference in the 
thoroughness and completeness Wiith which the facts 
have been examined. In many cases the common sense 
of to-day is simply the science of yesterday, for com- 
mon sense is usually very conservative, and often re- 
gards the novelty of a conclusion as an argument 
against it. 

Induction and Deduction included in Scientific 
Method. — Scientific method being simply a more thor- 
ough application of principles universally employed in 

1 Huxley, The Educational Value of the Natural History 
Sciences, 



INDUCTION AND DEDUCTION 3 

reasoning, a good means of getting a general view of 
those principles will be to examine the procedure of 
science. It includes both formal and inductive logic. 
Formal or deductive logic is simply one part of scien- 
tific method; hence any exposition of scientific method 
will include an examination of deduction. Sometimes 
induction is identified with scientific method, but it is 
often used in a narrower sense ; and, in any case, it 
might seem to exclude deduction, which is an essen- 
tial part of complete scientific method: therefore it 
is less confusing to think of induction as simply a part 
of scientific method. Inductive and deductive reason- 
ing are constituent elements in a single system. For 
purposes of study, it will be advisable to break up the 
system into several parts. The first of these parts will 
include the processes and principles involved in acquir- 
ing a knowledge^ of _fac^ ; the second, those employed 
in the classification of facts ; the third, includes the 
discovery and formulation of laws ; and the fourth, 
the testing of these laws and their further organiza- 
tion and application. Each of these processes will be 
found to involve a number of subsidiary processes. As 
they are parts of a system, they are, of course, mutu- 
ally dependent ; each leads up to or implies the 
others. 

The Beginning of Knowledge. — Nowadays there is 
almost universal agreement to the statement that all 
knowledge begins in the perception of concrete facts. 
It has sometimes been thought that the mind began 
its career with a capital stock of knowledge in the 
form of " innate " ideas or principles. But no one 
now maintains that there is any knowledge before ex- 



4 INTRODUCTORY 

perience begins. That, however, is no warrant for 
the conclusion which John Locke drew.^ He held that 
the mind, at the beginning of its history, is like a sheet 
of white paper or a waxen tablet or an empty cabinet, 
and that experience, like some external force, writes 
upon the tablet or fills the cabinet. To him the mind 
seemed to be passive in the acquisition of knowledge, 
able at most to combine and analyze its sensations and 
ideas. Immanuel Kant, on the other hand, contended ^ 
that, even in those mental operations in which the mind 
is seemingly least active, it is contributing essential 
elements ; that it makes knowledge, as it were, out of 
the material which is furnished from without ; it cannot 
operate without material, hence there is no knowledge 
before sense-experience begins ; but this sense-experi- 
ence itself is, in his view, a product of the mind's activ- 
ity. We cannot pursue this question any further; our 
concern is not with the philosophical problem of the 
ultimate source of knowledge ; it is enough for our 
purposes to know that knowledge begins in concrete 
experience, in perception, in knowing sounds and 
colors, odors, moving objects, pains, pleasures, emo- 
tions, and so on. 

Natural Sciences and Others. — Things and events 
and relations in the external world constitute the data 
of what are sometimes known as the " natural " sci- 
ences, such as biology, physics and chemistry. Mental 
facts and their relations make up the data of psychol- 
ogy; they are quite as concrete in their way as any 
physical facts, and the methods employed by psychol- 

2 In his Essay on the Human Understanding , 

3 In his Critique of the Pure Reason, 



THE SOURCES OF KNOWLEDGE 5 

ogists are the same as those used in the physical 
sciences. 

Such sciences illustrate almost all the processes em- 
ployed in the acquisition of knowledge, whereas a sci- 
ence like mathematics makes most use of a few of them, 
which it applies and elaborates with great thorough- 
ness. We shall attempt to follow, as closely as may be, 
the stages in building up knowledge as they appear in 
the natural sciences. As in knowledge generally, these 
sciences begin with the perception of facts, external or 
internal. Then sooner or later they proceed to classify 
and organize the knowledge thus gained. 

The Sources of Knowledge, Direct and Indirect. — 
Perception of concrete facts comes first as a source 
of knowledge, or rather as the primitive form of 
knowledge. Its limitations are obvious ; it is often far 
from clear ; it is frequently mistaken ; it embraces com- 
paratively few facts at any one time, and it does not 
extend beyond the present, or, at most, the immediate 
past. If we had to depend upon it alone, we could 
never get together a body of knowledge. It is possi- 
ble dimly to picture a mind which could be aware only 
of what was immediately present in time and space; 
its knowledge would be rudimentary, and without 
knowledge of something besides the present, the pres- 
ent itself would be meaningless. In all but the lowest 
types of consciousness there is a constant use of indi^ 
red means to 'knowledge. Memory is the first of these.^ 
Memory restores a larger or smaller part of the 

4 It might perhaps be said that memory is direct knowledge of 
the past, and this is true in a sense; but the dependence of memory 
upon previous perception, the fact that we do not remember what 
we have not previously perceived, shows that it is also indirect. 



6 INTRODUCTORY 

knowledge previously gained in perception, and thus 
makes It possible to draw upon past as well as present 
experience. 

Another indirect means to knowledge Is the testimony 
of others ; by this means we can come into possession 
of a knowledge of facts which have never come under 
our own observation. Oral reports and written rec- 
ords furnish incomparably more information than any 
man's unaided observation could afford. 

A further way of extending our knowledge is to be 
found in inference. From knowledge ^whlch we already 
possess we are able to arrive at conclusions which shall 
be true of things which may never have been observed 
by any one ; we infer the cause of a distant sound, or 
the character of the other side of the moon, or the 
stature and habits of man's remote ancestors, or the 
climate of the Northern Hemisphere In the Carbonifer- 
ous Age, etc. As we shall see later, inference is in- 
volved in greater or less degree in all the other means 
to knowledge. 

An inference may, of course, be wrong; If It Is to 
possess any degree of certainty, there must be a con- 
siderable body of information about the facts in ques- 
tion or about other facts closely related to them. The 
same is true, to a great extent, of memory, and even 
of perception, and to a very great extent in the case 
of testimony. Errors may arise at any point, and 
one of the most important problems in all thinking is 
the detection and elimination of errors. 

Organizing Knov^ledge. — Classification as a Pre- 
liminary Step. — So far, attention has been fixed upon 
the processes employed in acquiring knowledge of facts. 



LANGUAGE 7 

In order to make this knowledge available, the data 
thus acquired must be arranged or classified. The ob- 
ject of science is to get organized knowledge, and 
before knowledge can be organized it must be so ar- 
ranged as to enable us to see what facts are similar 
p.nd what are different. Classification is the grouping 
of phenomena according to their likenesses, and differ- 
ences ; those possessing a given characteristic are put 
into a group or class ; those lacking it may be put into 
one or more other classes. Classes may be grouped 
together in a larger class or subdivided into smaller 
ones. 

Language as a Necessary Instrument. — There is one 
very important instrument for the acquisition of 
knowledge which has not yet been mentioned ; and that 
is language. Without some means of describing or 
otherwise representing facts, only a very limited use 
could be made of our perceptions : testimony would be 
impossible without it ; inference involves representing 
to ourselves the consequences of certain principles or 
facts or situations ; imagination and memory are ways 
of representing what is absent by means of pictures of 
the facts themselves or by means of other symbols. A 
great variety of symbols might be employed, but lan- 
guage, spoken and written, supplies by far the most 
important and complete set of symbols. The descrip- 
tion and classification of facts would be practically 
impossible without language. 

Further Steps in Organized Knowledge. — In some 
sciences we find little more than classified knowledge; 
the so-called " classificatory sciences," such as botany 
and zoology, have, until recently, consisted almost 



8 INTRODUCTORY 

wholly of classified data. Science aims not simply at 
classified knowledge, but at organized knowledge, at 
knowledge organized into a coherent system.^ It aims 
at the discovery of the laws manifested by its data as 
well as at the discovery of the data themselves and 
their arrangement into groups. 

What is a scientific law? A law in the field of sci- 
ence is a statement of the way in which things do 
invariably behave. Unlike a moral law, a scientific 
law has nothing to say about the way in which things 
ought to behave, and, unlike a civil law, it does not 
prescribe a mode of action whose violation involves a 
penalty. The law of gravitation, for example, simply 
states that bodies do attract each other in certain defi- 
nite ways ; if bodies should fail to do this, the law of 
gravitation would be no genuine law. A scientific law 
states an invariable, unconditional connection between 
phenomena. 

How are laws of this character discovered.^ They 
are based originally upon observation of particular 
instances of the behavior of phenomena. From ob- 
served instances we draw an inference which covers all 
other cases of the sort, past and future. This, that 
and the other acid turns blue litmus paper red; we 
conclude that all acids will have a like effect. This 
conclusion may, of course, be mistaken ; it is an infer- 
ence, and must be tested or verified. 

Verification is then the next step. It may be under- 
taken in several ways: our conclusion may be com- 

5 There are of course fields of science where classified knowledge 
is the most that can be had. But the ideal of science goes beyond 
this. 



PRESUPPOSITIONS 9 

pared with other things which we know about the facts 
under investigation ; it may be shown to be a conse- 
quence of some known law ; or it may be possible to 
find some further fact which would be consistent with 
our inference and with no alternative inference that 
can be suggested. Speaking generally, verification in- 
volves finding whether the inference in question fits in 
with the system of things to which it belongs. If such 
a test cannot be applied, if there is no such system of 
which it can be shown to be a member, it remains 
uncertain. 

What is Presupposed? — One important question re- 
mains to be asked. Are there any laws or universal 
propositions which do not require verification .f^ Are 
there any statements which are self-evident and not 
open to question or to proof .^ Axioms, such as those 
of mathematics, are sometimes said to be of this char- 
acter. For example, take the statement that two 
things equal to the same thing are equal to each other ; 
can this statement be doubted or can a proof for it 
be conceived.^ Are there not propositions which are 
so fundamental that they cannot be based upon any 
which are more general, and so necessary to all thought 
that they cannot be based upon perception, but are 
presupposed in perception.^ This raises again the 
question at issue between Locke and Kant; without 
attempting to answer it, we may at least say that 
no proposition which does not justify itself in experi- 
ence can be accepted as true. Many propositions have 
seemed to be self-evident only to be proved false by 
later development in knowledge, and whatever else may 
be urged in favor of any proposition, it must at any 



10 INTRODUCTORY 

rate fit in with the rest of the things we know if it 
is to be accepted as true. 

Certain of these axioms or postulates are to be found 
in every science. In logic they appear under the name 
of the Laws of Thought. They are : 

The Law of Identity, expressed by the formula : A 
is A. 

The Law of Contradiction, expressed by the formula : 
A is not non-A. 

The Law of Excluded Middle: Either A is B or A 
is not B. 

The Law of Sufficient Reason: Every thing which 
exists has a sufficient reason or cause for being what 
it is. 

There is some disagreement regarding the meaning 
of some of these laws. The Law of Identity, for ex- 
ample, seems to be a mere tautology : to state that 
A is A, or that a thing is what it is, does not seem to 
give us any information. It is true, of course, that 
in a world where the Law of Identity, in this sense, 
did not hold, reason could do nothing. But the Law 
of Identity is usually taken to mean also that there 
must be an element of identity in every act of thought 
and in every piece of reasoning. In the proposition 
" Man is rational," it is obvious that man and rational 
are not identical; still there is something common to 
the two; without this core of identity no single judg- 
ment would be possible. 

The Law of Contradiction complements the Law of 
Identity.. A thing is not its opposite, and in so far 
as there is opposition between two things it is neces- 
sary to assert that one is not the other. 



THE LAWS OF THOUGHT 11 

The Law of Excluded Middle asserts that of two 
contradictory statements one or the other must be 
true. The law does not hold if the two statements are 
not contradictory, i.e,, if there is any third possibility. 
There is a middle ground between " A is brilliant " and 
" A is stupid " : he may be an average person. But 
" This figure is square " and " This figure is not 
square " are contradictories. 

All these laws are, of course, laws for thought, but 
they are equally laws of things, and they are laws 
for thought for that reason only. Certainly they 
must hold for any world in which reason can operate. 

The Law of Sufficient Reason asserts that the uni- 
verse is a rational universe; that for everything that 
exists there is a reason, and an adequate reason ; that 
things are capable of explanation, implying that the 
world is a coherent system. In the words of Leibniz, 
who gave the principle its rank, ". . . nothing 
occurs for which one having sufficient knowledge might 
not be able to give a sufficient reason why it is as it is 
and not otherwise." ^ If the world were entirely 
chaotic, knowledge, except that of the most primitive 
sort, would be impossible; there could be no general 
knowledge, no knowledge of laws or principles, for laws 
and principles would not exist. It is conceivable, how- 
ever, that the world is only partly rational, that there 
are things for which there is no sufficient reason ; if so, 
rational knowledge would be limited to the fields within 
which principles did hold. 

Summarizing, we may say that every science aims 

6 Principes de la Nature et de la Grace, Quoted in Dictionary 
of Philosophy, Ed. J. Mark Baldwin, Art. " Sufficient Reason." 



12 INTRODUCTORY 

at the discovery of the laws of the data with which 
it deals, and at the organization of all its content into 
a single systematic whole. A completely organized 
system of knowledge would be one in which every part 
would imply every other, and he who understood the 
system perfectly could reconstruct the whole from any 
part. Cuvier claimed that a naturalist could recon- 
struct an animal from a single bone, and he himself, 
as noted by Huxley in the passage quoted above, gave 
evidence of the validity of his claim. Perfection of 
organization is not to be found in any natural science; 
the mathematical sciences show something approxi- 
mating completeness, but they do not de^l directly w^ith 
concrete facts. 



CHAPTER II 
FIRST STAGES IN KNOWLEDGE 

I. Facts and the Ways in Which They are Known. — 
Knowledge begins with the perception of facts; and 
these facts are of many kinds. What is a fact? 
A fact is anything which exists ; it is that which 
is real, apart from any opinion we may have about it 
or any attitude which we may take toward it ; it is 
that which is as opposed to that which is merely imag- 
ined or conceived. When we ask for facts, we ask for 
something which shall be independent of any belief ^ or 
disbelief, approval or disapproval, on the part of any 
person.^ Some or all of these characteristics belong to 
laws, but fact is distinguished from law in being con- 
crete and particular, instead of abstract and general. 

A. Perception and What It Includes. — Facts 
are known primarily through perception and memory; 
they are known directly only by means of perception, 

1 Belief and disbelief, whether true or false, are themselves 
facts; they are psychological facts. Belief in the Ptolemaic as- 
tronomy was a fact; that is, the belief actually existed. A false 
belief is one in which the thing believed is not a fact; it asserts 
or assents to something which does not really exist. Belief or dis- 
belief may bring about changes in facts ; in other words, give rise 
to new facts, as may any other existing thing. To say that a fact 
is independent of our attitude means that its existence and char- 
acter are what they are apart from our attitude and aside from 
any possible effects which may be produced upon them by our 
attitude. 

2 This position is confessedly dogmatic. Further reflection 
might show that nothing is independent, but for our present pur- 
pose this position is justified. 

13 



U FIRST STAGES IN KNOWLEDGE 

though there are various ways in which they may be 
known indirectly. One of the most important of these 
indirect means, and one which is an important element 
in all the rest, is inference; a perceived fact may be 
evidence to our minds of the existence of something 
which we cannot perceive. 

Much that is often included under perception must 
be eliminated when we are trying to use the term with 
scientific accuracy. For example, we say that we per- 
ceive the inkstand upon the table, or a man on the 
other side of the street, or that lightning has set fire 
to a distant building, or that Mr. ,X is an able law- 
yer, or that history repeats itself, and so on. Are any 
of these pure perceptions.^ We may perceive certain 
events^ but to " perceive '' that history is therein re- 
peating itself involves, at the very least, these infer- 
ences : that the words of historians represent what has 
occurred in the past ; that they are competent and 
truthful and that we understand them ; and that the 
events we perceive are really like those which they have 
described. In the example of the lawyer, we base our 
belief on observation of certain acts of his which have 
brought about desired results in spite of difficulties ; 
and on the inferences that he understood the situation 
and intended to bring about the results which actually 
occurred. Again, though the flash and the distant 
light were perceived, the conclusions that the flash was 
lightning and that the light was that of a burning 
building in the distance, and that the first of these was 
the cause of the second, involve far more than percep- 
tion. In such instances as these the presence of infer- 
ence is evident and the importance of distinguishing 



PERCEPTION AND INFERENCE 15 

what is perceived from what is inferred is obvious. 
The perception might be correct, while the inference 
was erroneous, or vice versa. By distinguishing the 
two, the problems of discovering error and of correct- 
ing it are much simplified. 

But it is by no means easy to know where to draw 
the line between perception and inference. We should 
say ordinarily that we perceive the ink-well or the man 
across the street, but even in these cases there is some- 
thing which is very like inference. A perception con- 
tains many different elements, and these get themselves 
before the mind in a variety of ways ; comparatively 
little in any perception can be said to come directly 
from the object. In the perception of the ink-well or 
the man all that we get directly is a spot of color 
with certain variations of light, shade, and so on. But 
we seem to see an object in three dimensions, of a cer- 
tain size, at a given distance from us, and possessing 
weight, resistance, a certain degree of hardness, a pe- 
culiar internal structure and an indefinite number of 
other qualities, which may be more or less definitely 
present to the mind. If we had not, in the past, found 
these qualities in combination with spots of color sim- 
ilar to those now present, we should not be aware of 
them now ; but that does not mean that these qualities 
are simply remembered, for they are present to the 
mind as genuinely objective qualities^ and we seem to 
be as directly aware of them as we are of the color, 
although reflection shows us that they could not be 
given by sight alone. They all seem to present them- 
selves together, while in remembering a number of 
events, first one appears before the mind and then an- 



16 FIRST STAGES IN KNOWLEDGE 

other ; in perceiving an object, the quaHties do not come 
forward one after another, but all seem to be present 
together in a single thing. A perception is a reaction 
of the mind to an object, quality, or event of some kind. 
A mind which has had little experience in a given field 
will react to an object in that field with a perception 
of a comparatively simple sort ; if one had seen and 
handled oranges but had not tasted them, his percep- 
tion would contain no suggestion of the flavor, as a 
blind man's perception contains no suggestion of color 
or other visual qualities. 

Every time an object is perceived under new condi- 
tions something is added which will modify future per- 
ceptions in greater or less degree. The child builds up 
his perceptions gradually ; from a first vague, indefi- 
nite perception he advances to one that is more coher- 
ent and complete. 

The way in which any person will perceive an object 
will depend largely upon his past experience : different 
persons will consequently perceive the same object dif- 
ferently ; as no two persons have ever had precisely 
the same experience, they will never see a given object 
in precisely the same way. But in most instances the 
diff'erences will be slight, because there is so much that 
is common in the experience of all, and in the percep- 
tion of ordinary objects the diff'erences are usually 
small and comparatively unimportant. 

" Fallacies " of Perception, and Their Causes, — ^We 
think of perception as a certain and infallible source 
of knowledge ; but if in all perceptions there Is a large 
addition from past experience it is clear that many 
of them are likely to be wrong. The present object may 



CAUSES OF MISTAKEN PERCEPTIONS 17 

not be similar in all respects to like objects which we 
have seen in the past. A spot of color of a certain 
shape and apparent size may have stood invariably 
for an orange ; in other words, it may have been found 
along with other sensations indicating a solid spherical 
object, of a certain flavor and odor, with a certain in- 
ternal structure, and so on. If the spot of color again 
appears we seem to be aware of the other qualities. 
But there may be only a spot of color, as on the 
painter's canvas. Again, when two persons are similar 
in appearance, one may easily be mistaken for the 
other. The visual appearance of A may seem to as- 
sure the presence of the other qualities which, as a 
matter of fact, belong to B. 

The possibility of erroneous perceptions was com- 
mented upon very early in the history of thought, and 
because errors of this sort occur so frequently, some 
thinkers concluded that the senses were altogether unre- 
liable as sources of knowledge. Others urged that the 
fault was not with the senses ; they pointed out that 
the trouble lay in adding to what the senses gave. 
When we have a sensation of greenness, they said, 
greenness is actually present to the mind ; if we go on 
to say that there is present an apple, we are adding a 
number of qualities to those which are given by sensa- 
tion, and the qualities we add may not really be there. 
If we should refrain from adding those other qualities 
we should never be mistaken, but it is impossible en- 
tirely to separate the sensational element from the 
others. The perception is a unit in spite of the com- 
plexity of the qualities which make it up, and these 
qualities are capable of modifying each other. The 



18 FIRST STAGES IN KNOWLEDGE 

green of a picture or of a landscape does not look the 
same if the scene Is looked at upside down ; of course 
we should be correct in saying that w^e seem to see a 
certain shade of green in the first case and a different 
one in the second. We may be perfectly certain with 
regard to what we seem to see ; but then we seem to see 
an object as having three dimensions, when it may have 
only two, as in a painting; what we usually want to 
know is whether we see the thing as it is, whether other 
people seem to see the same thing, whether we may 
expect to seem to see it in the future, whether handling 
the object would give confirmatory sensations, and so 
on. The attempt to limit our statements to what is 
unmistakably before the mind takes us a very little 
way toward certainty in knowledge. Perceptions in- 
clude more than that. They should, of course, be made 
as carefully as possible. But although errors are cer- 
tain to occur, yet if we do not run this risk of error we 
make little progress toward knowledge. 

This first form then in which knowledge appears is 
open to mistake ; there are mistaken perceptions. It 
may be well to note the different types of error and 
their chief causes. The types are usually said to be 
two ; and they have been called Mal-observation and 
Non-observation. The names are self-explanatory. 
Mal-observation is of two kinds : in the one, something 
which does not belong to the object is added in the 
perception ; in the other, the relations of the parts are 
wrongly perceived, as when we read there for three. 
Of course, both kinds of mal-observation may be pres- 
ent together, and non-observation also. Otherwise 
stated, there are really three kinds of error: omission. 



THREE KINDS OF ERROR 19 

addition and wrong relation of the parts in a whole. 
They may occur at any stage in knowledge, and they 
are, in fact, the only kinds which can occur at any 
stage. What are their causes in the field of percep- 
tion? A passage from Bacon, quoted by Jevons, calls 
attention to a number of the causes which give rise to 
them: "Things escape the senses because the object 
is not sufficient in quantity to strike the sense: as all 
minute bodies; because the percussion of the object is 
too great to be endured by the senses: as the form of 
the sun when looking directly at it in mid-day ; be- 
cause the time is not proportionate to actuate the 
sense: as the motion of a bullet in the air, or the quick 
circular motion of a fire-brand, which are too fast, or 
the hour hand of a common clock, which is too slow; 
from the distance of the object as to place: as the size 
of celestial bodies, and the size and nature of all dis- 
tant bodies; from prepossession by another object: as 
one powerful smell renders other smells in the same 
room imperceptible; from the interruption of interpos- 
ing bodies : as the internal parts of animals ; and be- 
cause the object is unfit to make an impression upon 
the sense: as the air, or the invisible and untangible 
spirit which is included in every living body." 

The various kinds of causes may be classified as 
follows : 

1. In the first place, the external or physical con- 
ditions of the perception may be unfavorable ; in a red 
or green light, the color of objects is wrongly seen; 
in a fog, sounding objects seem nearer than they really 
are; if the light is dim, details are overlooked; if we 
look through an imperfect window-pane, objects ap- 



20 FIRST STAGES IN KNOWLEDGE 

pear distorted. In all these cases there Is something in 
the medium through which the object is perceived 
which leads to error. Similar difficulties arise when 
instruments are emploj^ed to extend the range or in- 
crease the accuracy of our perceptions. Any imper- 
fection in the instrument is almost certain to be a fruit- 
ful source of error. Other things might be cited in 
this field, but these will suffice to illustrate the class. 

2. Next in order we may mention the physiological 
causes of mistaken perceptions. Imperfections in the 
sense-organ, fatigue, illness, and the like are obvious 
examples. There is one sort of perception which is 
always inaccurate, that of the time at which an event 
occurs ; a flash of lightning is seen a fraction of a 
second after the light reaches our eyes ; a sound is not 
heard in the instant at which it reaches our ears. The 
reason is this : a thing cannot be perceived until the 
nerve current which it sets up in our sense-organ has 
passed along through the nerves to the brain; this 
takes time, and in some cases, as in astronomy, the 
errors which arise from this source may be very im- 
portant. Again, we often tend to perceive an event 
for a moment after it has ceased, since the nervous 
system continues to reverberate, as it were, after the 
original cause of its activity has ceased to act. Hence 
the flash or sound seems to be present after it has 
really passed. This is seen in our inability to distin- 
guish the spokes of a rapidly revolving wheel or the 
successive vibrations of a tone, or single views In mov- 
ing pictures ; in all these the succeeding event begins 
before we have ceased to perceive the one before It. 

3. But if all physiological and physical conditions 



PSYCHOLOGICAL CAUSES OF ERROR 21 

were favorable, if all organs and media and instru- 
ments were perfect, there would still remain the psycho- 
logical sources of error. These are often or even 
always present along with the others. One of the psy- 
chological causes has already been alluded to, namely, 
(1) the tendency to see what we have previously seen 
in similar circumstances. There is also (2) a tendency 
to perceive what we expect or wish or hope or fear, or 
what has been recently or habitually in the mind, or 
that which has been vividly perceived or imagined. 
What is known as the " proof-reader's " illusion illus- 
trates one of these ; in reading, the context often sug- 
gests a certain word and we see that word and 
overlook mistakes in spelling. In the following passage 
(based on one in James's Psychology) few persons 
reading at the ordinary rate, and with ordinary care, 
would succeed in detecting all the mistakes in spelling: 
Any one wateing in a dark plase and expectng or faer- 
ing a certaon objectt will interpret an abrup sensation 
to mean that object's presense. The boy playing " I 
spy," the criminel skulhing from his persuers, the 
superstitions personn hureying throuh the churchvard 
at midnight, the man losst in the woods, the girl who 
tremulusly has made an evening apointmnt with her 
swain, all are subjec to ilusions of sight and sound 
wkich make there hearts beat til they ate dispelld. 

Another case illustrating some of these principles is 
that of the prisoner who had already been convicted 
of one crime and served his sentence, and who narrowly 
escaped conviction a second time, although entirely 
innocent in both cases. He bore a superficial resem- 
blance to the real criminal ; the witnesses were predis- 



22 FIRST STAGES IN KNOWLEDGE 

posed to believe that he was the criminal, and they 
positively identified him as the one whom they had seen 
committing the crime. 

The effectiveness of all these tendencies is enhanced 
by (3) lack of attention or misplaced attention. The 
inattentive reader overlooks misprints, and so does the 
reader who is very intent upon the thought. Presti- 
digitators, fraudulent spiritualistic mediums, and the 
like, take advantage of these tendencies. They direct 
attention to unimportant things in order that they 
may do the important ones unobserved, and by leading 
the spectator to expect certain events they can often 
persuade him to believe that he actually witnesses them. 

Mistakes as to the order of events are very easy in 
some circumstances ; if two events, one in the field of 
sight and the other in that of sound, occur very nearly 
at the same time, this often happens. (4) Lack of 
training in observing events of a given kind may make 
correct perception impossible ; the use of the micro- 
scope, finding and following a trail in the woods, 
seeing distant objects at sea or on the plains, distin- 
guishing flavors, colors, etc., are examples. 

(5) Abnormal psychological conditions, such as 
nervous excitement, those produced by drugs, etc., 
modify the keenness and accuracy of perceptions, 
sometimes for the better and sometimes for the worse. 
These various causes, physical, physiological and psy- 
chological, are so closely bound up together that it is 
often difficult to say which is chiefly operative in any 
given case. 

Careful and intelligent attention will prevent many 
errors. A careful perception mad© with a purpose is 



OBSERVATION 23 

called an observation. This term is sometimes used to 
cover all perception whatsoever, but it will be used 
here in the narrower sense. Still, the most carefully 
made perception may prove to be mistaken. In some 
of the sciences there are various special and technical 
methods of eliminating error.^ 

The discovery of error does not always lead to its 
elimination nor enable us to make the requisite correc- 
tion. In some cases it does ; we have already seen that 
the perception of an event takes time ; this time is 
longer for some persons than for others, but for each 
it is approximately constant under given conditions. 
By means of a device which registers the exact time at 
which a certain event occurs and the time at which the 
observer indicates that he perceives it, it is possible to 
determine his " personal error " and to make the 
proper correction in cases in which the exact time of 
the occurrence cannot be otherwise determined. But 
in most cases it is not possible to do this or even to 
guess at the presence or the amount of error. Some- 
times, as in the case of measurements, it may be pos- 
sible to repeat the observation, and if the results 
cannot be made to agree, we can sometimes get a result 
approximately correct by taking an average. 

Testing Perceptions, — It can almost be said that 
every observation should be held in suspicion until 
tested. The test would consist in finding out whether 
it agreed with other observations of the same fact or 
of similar facts made by ourselves or others, whether it 
was in agreement with the laws of the field in which it 
was found, with the laws of Nature generally, and so 
3 See Jevons, Principles of Science, chap. xv. 



^x. 



M FIRST STAGES IN KNOWLEDGE 

on. We always proceed upon the principle that all 
knowledge should hang together, should be consistent 
and coherent ; that the world is a consistent and 
coherent world; and that correct perceptions will 
agree with each other and with the rest of our expe- 
rience. 

When it is possible to repeat an observation, we have 
at once a starting-point for testing it ; and when new 
observations can be made under more exact conditions, 
we are in a very favorable position for extending our 
knowledge of the facts under observation. One of the 
chief reasons why modern astronomy, for example, is 
so far in advance of that of the Greeks is to be found 
in the fact that modern instruments make the observa- 
tions of astronomical phenomena so much more reli- 
able. 

Experiment, — Sometimes it is possible to reproduce 
at will the ph^enomenon under observation. This is the 
case, to a great degree, in physics and chemistry: 
sounds, chemical changes, and so on, can be repeated 
indefinitely. Moreover, the circumstances in which the 
phenomenon occurs may often be controlled and varied 
more or less, and that is very often a matter of great 
importance, as will appear later. To bring about an 
event for the sake of observing it is to experiment. 
An experiment may be performed for various reasons ; 
it may be that we wish simply to get an additional ob- 
servation as a basis for inference or a means of testing 
the accuracy of one which we have made already ; or 
we may wish to see the result of changing certain of 
the circumstances in which the phenomenon occurs ; or 
of finding the consequences of any condition whatso- 



EXPERIMENT 25 

ever. " Whenever we can, by our own agency, influence 
the object we are investigating, we can remedy this 
wsint [insufficient observation] by experiment. We 
can institute at will a certain group of conditions C, 
and so compel the causes which are really at work to 
respond with an effect E, which would otherwise per- 
haps have never come within the domain of our senses. 
By varying at will the quantity and composition of 
that C we can bring about in E a series of changes in 
quantity and kind, which were still less likely to offer 
themselves unsolicited to our observation. Again, we 
can break up C into its component parts, and in each 
experiment allow but one of these, or a definitely as- 
signed group of several of them, to take effect, at the 
same time cutting off the rest from action. The con- 
stituent elements of the result E admit of being sepa- 
rated in the same way, so that we learn which of them 
depends upon which element of the compound C. Thus 
experiment is the practical means by which we furnish 
ourselves with observations in such number and involv- 
ing such mutual differences and affinities as is requisite 
in order to the elimination of what is unessential in 
them. . . . Defined in this way, it is clear that ex- 
periment only has an advantage over observation in so 
far as it is capable of supplementing the usual defi- 
ciencies of the latter ; its function is to furnish us with 
suitable and fruitful observations instead of the un- 
suitable and unfruitful ones which offer themselves. 
. . . It is merely a way of preparing and setting be- 
fore ourselves phenomena which it is of importance that 
we should observe." ^ But its function is exceedingly 
4 Lotze, Logic, Bk. II, chap, vii, 260. 



26 FIRST STAGES IN KNOWLEDGE 

important, and without it many sciences could make lit- 
tle progress. 

The peculiar advantage of being able to control and 
vary the conditions of an event to be observed will be 
evident at a later point. 

B. Indirect Means to Knowledge of Facts. 
I. Memory and its Defects, — So far in the present 
chapter we have discussed only the direct means of 
knowing facts. It appeared, however, that even in per- 
ception there is much that is a revival of past experi- 
ence, reinstated by the memory. Knowledge of the past, 
reappearing in memory, bulks very large in the total of 
our knowledge. True memory is simply the recall of 
past experience accompanied by awareness of the fact 
that it was our experience. If one experience or one 
object of experience is similar to what is now before 
our minds, or if it has been related to the latter in 
any way, it tends to reappear. That tendency is often 
overcome, otherwise practically everything would be 
remembered. Not only do many things drop out of the 
memory, but many are also changed in their character 
OT order, and some things may be added. Ordinary for- 
getfulness corresponds to non-observation. It is prac- 
tically always present in greater or less degree, and 
it obviously tends to increase with the lapse of time. 
Many things disappear altogether; sometimes the main 
outlines are remembered and details forgotten ; some- 
times only a few of the details remain. 

Remembering wrongly corresponds to mal-observa- 
tion : words which were correctly heard may be incor- 
rectly remembered; an object which was seen as red 
may be remembered as brown, and so on. Hardly ever 



DEFECTS OF MEMORY 27 

do any two witnesses agree exactly in their memory of 
events which could easily have been observed with little 
danger of mistake. This is so generally recognized 
that too close a correspondence between the stories of 
two witnesses is regarded as an evidence of collusion 
and dishonesty. 

Besides the modification of details, the order of 
events may be changed in memory or their relations may 
be modified in other ways, and entirely new elements 
may be introduced. Among the causes of mistaken 
memory the following may be noted: 

1. A tendency to remember what would usually have 
happened in the circumstances. 

2. A tendency to remember things or elements which 
were particularly pleasant or unpleasant, desired or 
feared, etc., at the expense of those which were more 
neutral. Elements or events of this sort, which did not 
occur but were suggested or expected, may be remem- 
bered as if they had occurred. 

3. A tendency to remember things in a way which 
would make them more complete or logical, or more in 
agreement with our own opinions or wishes, or more in 
harmony with what we expected, or feared, etc. 

4. Events which have often been described in one's 
hearing may seem to be remembered. 

The tests of memory, like those of perception, are 
based upon the principle that genuine knowledge is 
always consistent and coherent, that the world of facts 
is throughout harmonious. 

Where accurate records are available the memory, 
as a source of knowledge of the past, becomes much 
less important. Accurate records made at the time 



28 FIRST STAGES IN KNOWLEDGE 

when the phenomena were perceived are an essential 
part of all the concrete sciences. The methods of re- 
cording are many, and they are too technical for pres- 
ent discussion. 

II. Testimony. — Written records and oral reports 
make up a large part of what is known as evidence. 
Besides these, evidence includes historical remains of 
every sort, products of man's activity, natural phe- 
nomena of every kind, such as glacial scratches, geo- 
logical deposits, etc., etc. The evidence may be of 
something in the remote past, of something not ob- 
served in the present, or of future events. The use of 
evidence clearly involves making inferences ; it also in- 
volves perception. Some phenomenon is perceived, such 
as an uttered sound or an inscription or a fossil, and 
on the basis of this perception the observer draws con- 
clusions concerning something which may never be per- 
ceived. 

Oral and written reports, or, in other words, testi- 
mony, furnish a frequent ground of inference. Testi- 
mony includes every statement of fact made by any 
one. The opportunities for error in using it are so 
numerous that it is surprising that correct information 
can ever be reached by means of it. 

1. In the first place, the person making the state- 
ment was liable to error in many ways when he observed 
the fact which his statement purports to represent. 

2. In the second place, his memory is almost cer- 
tainly inaccurate in one way or another. 

3. Again, the words which he uses may not correctly 
represent to us what he has in mind ; he may not use 
words accurately, or he may use them in a sense unfa- 
miliar to his hearer. 



DEFECTS OF TESTIMONY 29 

4. In the fourth place, he may not be truthful ; he 
may never have witnessed what he pretends to report, 
or he may intentionally misrepresent what he has wit- 
nessed. 

These difSculties are present in both oral and written 
testimony ; in the latter there are additional difficulties. 
What seems to be the witness of one person may be 
a garbled account ; or errors may have been intro- 
duced by a copyist or an editor. In oral testimony 
cross-examination gives a basis for testing statements 
of the witness. In written testimony the substitute for 
this is found in other statements by the same writers 
and by contemporaries ; when these are not to be found, 
little credence can be given to the testimony. 

III. Inference, — Inferences from facts of every sort 
are also liable to error. In every case the final test 
is that of consistency and coherency. The application 
of the tests very often involves complicated reasoning 
and a large body of special information ; it will be 
discussed incidentally in later chapters ; much of sci- 
entific method is for the purpose of making such tests. 

EXERCISES 

1. How much is really observed in seeing a marksman 
shoot a clay pigeon? In hearing an automobile pass^ a 
block away? In seeing a prestidigitator take an object 
from a pocket in which it was not? 

2. What are the causes of mal-observation and non-ob- 
servation in the following cases ? 

(1) A straight stick partly immersed in water seems 

to be bent. 

(2) Two objects looked at through a stereoscope 

seem to be one^ and they seem to be solid in- 
stead of flat. 

(3) The sun seen through a fog sometimes appears 

red. 



30 



FIRST STAGES IN KNOWLEDGE 



(4) Mirrors increase the apparent size of a room. 

(5) Distant objects appear small. 

(6) Patients often seem to feel pain in amputated 

limbs. 

(7) A table seems to throb if the fingers are pressed 

against it. 

(8) A rearrangement of the furniture in a room is 

often unnoticed. 

(9) We sometimes seem to feel the motion of a boat 

after landing. 

(10) There are marked differences in what the ordi- 

nary good observer^ the artist_, and the botanist 
'* see in a flower. 

(11) Silas Marner mistook Effie's hair for the lost 

gold. 

(12) Looking at one's watch and not knowing the 

time a moment later. 

(13) Not seeing the people one meets. 

(14) In Poe's S'phinx, a small animal on the window- 

pane is thought to be a large moth of a strange 
species. 

(15) Mistaking the order of numbers^ as 5^Q for 56^. 

(16) Finding a likeness between an infant and its 

parents. 

(17) Macbeth seeing Birnam Wood coming to Dunsi- 

nane. 

(18) The pain of amputation when^ instead of am- 

putation^ an icicle is drawn across a limb. 

(19) Shooting a man for a deer when hunting in the 

woods. 

(20) The child's " seeing '* things at night. 

8. Give five examples of mistaken observation arising 
from each kind of cause described in the text. 

4. Suggest causes for errors of memory in the follow- 
ing cases: 

(1) Memory of "the good old days '' as better than 

the present. 

(2) Remembering the childhood of men who later 

became famous. 



EXERCISES 31 

(3) In Ivanhoe, Wamba tells the travelers to go in 

one direction^ but points in the other; one of 
them remembers the verbal directions,, the 
other the direction pointed out. 

(4) Forgetting cases which do not support one's 

view. 

(5) Forgetting certain items in lists of things to be 

bought^ etc. 

(6) Dropping out characters or events in remember- 

ing a story or play. 

(7) Ascribing to one person words or deeds of an- 

other. 

(8) ** Remembering " events which occurred before 

one was born. 

(9) " Remembering " the apt replies which one 

might have made. 
(10) Remembering as an actual experience what was 
merely a fiction often related as an experi- 
ence. 

5. In how many different ways could you account for 
the statement of a witness that he had seen a ghost? 

6. Suppose three honest witnesses to have testified to 
seeing a man catch a bullet in his teeth: What would 
your conclusion be? 

7. How would you test the statement: General X was 
killed in the battle of Gettysburg? 



CHAPTER III 
CLASSIFICATION 

Objects of experience make their appearance in an 
order which seems to be almost chaotic ; and in memory 
they are often reproduced very much in the order in 
which they originally occurred. But even in memory, 
and still more in reflection, there is a tendency to 
arrange things according to their likenesses and diff*er- 
ences. This is the beginning of classification. Classi- 
fication " is not identical with collection. It denotes 
the systematic association of kindred facts, the collec- 
tion, not of all, but of relevant and crucial facts." ^ 

A classification is necessarily based on a similarity 
of some sort: of quality or structure or origin, and so 
on. Any given collection of things may be classified 
in many diff'erent ways. Books, for example, may be 
grouped according to subject, size, style of binding, 
publisher, and so on ; minerals, according to composi- 
tion, value or chemical properties ; the people of a city, 
according to race, income, occupation or religion. Any 
quality or relation whatever may serve as a basis of 
classification. In the abstract, one may be as good as 
another, and the one to be employed in a given instance 
will be that which best serves the purpose we have in 
hand. There are several diff'erent types of classification, 
each serving a special purpose. 

Types of Classification. — 1. Index Classification. — 

1 Karl Pearson, The Grammar of Science, chap. III., n. 1. 

32 



CLASSIFICATION 33 



59 2 



We may notice briefly the " Index Classification. 
The purpose of this mode of grouping is to enable us 
to get hold of a given fact quickly and easily. Cata- 
logues are usually constructed with this end in view, 
and they illustrate the principles involved. Certain 
obvious characteristics are selected, and very often a 
given item may appear under several diff*erent heads, 
as in cross-references. Alphabetical catalogues are the 
most familiar examples of the index classification. 

2, Diagnostic Classification. — A second type is 
the " Diagnostic Classification " ; its purpose is the 
identification of an object or the discovery of the group 
to which it belongs. " Nature Study " books abound 
in classifications of this sort. Here, too, certain obvi- 
ous characteristics are made the basis of classification. 
Flowers, for example, may be classified according to 
color or time of appearance or habitat ; or the main 
divisions may be made upon one basis, as color, the first 
subdivision on another, as time of appearance, etc. The 
identification of ailments by the physician depends 
upon a classification of symptoms made upon this plan, 

3. " Natural " and " Artificial " Classifications. 
— Both index and diagnostic classifications are useful, 
but they do not, by themselves, lead directly to any 
greater knowledge of the facts ot of their essential re- 
lations. They are based, for the greater part, upon 
superficial and easily noticed characteristics,^ and have 
little relation to the essential properties of the things 
classified. It is often possible, however, so to group 

2 See Jevons, Principles of Science, chap. xxx. 

3 A diagnostic classification which is to be a sure means for the 
identification of any and all cases should be based on essential 
qualities. Those based on superficial and striking qualities serve 



34 CLASSIFICATION 

phenomena as to display at once their most significant 
characteristics. Compare, for example, the popular 
classification of the whale as a fish with the scientific 
classification of the same animal as a mammal. To call 
a whale a fish is to imply that it lives in the water, but 
tells little more ; to call it a mammal tells us that it has 
warm blood, lungs instead of gills, a four-chambered 
heart, certain peculiarities of the skeleton, and so on. 

Grouping data in such a way as to make manifest 
at once their essential characteristics is the aim of 
classification in science. Since science aims at complete 
and systematic knowledge, it will obviously select as 
the basis of classification in any given case that quality 
which does correlate the greatest amount of knowledge 
about the facts under consideration. 

Scientists usually make a distinction between " arti- 
ficial " and " natural " classifications. " It would be 
possible to classify all living things according to color, 
as white, yellow, green organisms, etc. Such a classifi- 
cation would, however, be artificial and destitute of sci- 
entific value because based upon a purely artificial and 
highly inconstant character. An interesting example 
of an artificial classification formerly employed is the 
system of Linnaeus, who classified flowering plants into 
Monandria, Diandria, Triandria, Tetrandria, etc., ac- 
cording to the number of stamens. This was sufficiently 
convenient for a first rough arrangement, but was soon 
found to lead to the most incongruous association of 
plants agreeing in the number of stamens but diff*ering 
in almost all characters. From such cases it is plain 
that plants and animals cannot be naturally classified 

for ready identification of many cases, but not for all. See Bosan- 
quet's Logic for a discussion of Diagnostic Classification as one 
based upon deeper and more essential qualities. 



NATURAL CLASSIFICATIONS 35 

by likenesses or differences in a single character arti- 
ficially selected. The entire organisms must be taken 
into account, and the natural classification differs from 
the artificial one in representing real relationship and 
not merely superficial likeness. Modern biology teaches 
that this relationship is of precisely the same nature 
as human relationship, i.e,, that it is due to community 
of descent from ancestral plants or animals. 
The labor of determining the natural classification is 
much lightened by the fact that certain structures are 
often found as a matter of experience to be constantly 
associated or correlated, so that the presence of one 
indicates the presence of the others. In such cases a 
single character may be taken as the basis of a classi- 
fication which is natural, because agreement in one 
character has been previously proved empirically to in- 
dicate agreement in the others. For example, it has 
been proved that the differences or resemblances of ani- 
mals are correlated with corresponding differences or 
resemblances in their teeth. Hence mammals, to a great 
extent, can be classified according to the structure and 
disposition of the teeth. And so in many groups it 
is usually possible to discover empirically some one or 
few characters on which, by reason of their constant 
association with other characters, a natural classifica- 
tion can be based." ^ 

Biology furnishes one of the best illustrations of a 
field in which a natural classification can be made, al- 
though even here in many cases there is no universal 
agreement as to which is the natural classification. For 
each of two characters or sets of characters might be 
correlated with a number of others, and it might be 
4 Sedgwick and Wilson, Biology, p. 175. 



36 CLASSIFICATION 

difficult to decide which of the two correlated the 
greater number or the more important ones. Even if 
there were such agreement, it would not necessarily be 
permanent ; new information might result in the selec- 
tion of a new basis of relationship. The difference be- 
tween natural and artificial classifications is, as Jevons 
points out, one of degree only : " It will be found al- 
most impossible to arrange objects according to any 
circumstance without finding that some correlation of 
other circumstances is thus made apparent." 

The principle employed in classification for scientific 
purposes is well stated in Huxley's definition, which was 
modified somewhat by Jevons and stated in the follow- 
ing form : " By the classification of any series of ob- 
jects is meant the actual or ideal arrangement together 
of those things which are like and the separation of 
those which are unlike, the purpose of the arrangement 
being, primarily, to disclose the correlations or laws of 
union of properties and circumstances, and, secondarily, 
to facilitate the operations of the mind in clearly con- 
ceiving and retaining in memory the characters of the 
objects in question." 

A scientific classification is ordinarily designed to 
serve the purposes here enumerated, but there may be 
cases, especially in everyday life, where our primary 
interest is not in getting a complete knowledge of 
things, but in getting together things which have a re- 
lation to some common purpose or problem ; and in such 
cases the grouping together of things which are, in 
most respects, very dissimilar, may be justifiable. 
Custom-house regulations, for example, proverbially 
group together things which, apart from certain eco- 
nomic considerations, may be totally unlike. The so- 



DIVISION 37 

called artificial classification may be entirely satisfac- 
tory as an index or diagnostic classification, though in 
a diagnostic classification, as we have seen, the use of 
essential qualities would furnish a surer means for iden- 
tifying doubtful cases than the use of obvious qualities. 

Classification, of whatever sort, is not simply bring- 
ing together data into a single group ; it involves the 
further ordering of the data in sub-groups. 

Division. — Breaking up the group into sub-groups 
is known in logic as " Division." The first thing to do 
in making a logical division is to select some charac- 
teristic which will serve to distinguish some members 
of the group from the rest. It may belong to some 
and not to others, or it may belong to all in different 
degrees, etc. The technical name of a character used 
for this purpose is fundamentum divisionis, or basis 
of division. The simplest sort of division is that in 
which the fundamentum divisionis is a character pres- 
ent in some members of the class and lacking in the rest. 
Material substances may be divided into those which 
are mineral and those which are not ; or, to cite an 
ancient example, we may divide and subdivide sub- 
stances as follows : ^ 

Substance 

/ ' N 

Corporeal Incorporeal 

> ' ^ 

Animate Inanimate 

, ' . 

Sensible Insensible 

/ ^ > 

Rational Irrational^ etc. 

5 This is known as the Tree of Porphyry, so-named from the 
Greek logician who was the earliest writer to give a distinct ac- 
count of this type of division. 



38 



CLASSIFICATION 



Division of this kind is called dichotomous or bifur- 
cate, from the fact that each group or sub-group is 
always divided into two. 

A more complex classification results from selecting 
as the basis of division some character which is pos- 
sessed by all the members of the class but with differ- 
ences of degree or quality, etc. Books, for example, 
If classified according to subject matter, would fall into 
several groups, and each of these might again be sub- 
divided into several more.^ A dichotomous division 

6 As further examples of classification of this kind we may cite 
the following from Hyslop's Logic, pages 96, 97. 



Plane. 



Figures -{ 



Solid. 



' Physical. 



Science . . 



. Moral . . 



Rectilinear. 



Curvilinear . 



Rectilinear . 



Curvilinear . 



Trilateral 

Quadrilateral 

Multilateral 

r Circular 
] Elliptical 

Parabolic 

Hyperbolic 

Tetrahedrons 
Pentahedrons 
Cubes 
Parallelopipeds, etc„ 

Spheres 
Cones 
Cylinders 
Paraboloids 



I Phvsics 
Mechanical... I ^j^^^.^^^y 



i Organic | Sl'^^^'.^T 

•- I Physiology 

Po™cal {Sdol7gy 

r Noetics 
I Psychological . -{ Aesthetics 

[Ethics 



DICHOTOMOUS DIVISION 39 

would, of course, be possible here ; we might have some- 
thing like the following : 

Books 



f — ^ 

On history Not on history 

On chemistry Not on chemistry^ etc. 

But a dichotomous division would soon become un- 
wieldly ; moreover, it does not present the classes in such 
a way as to indicate which are coordinate. The ex- 
ample just given might seem to make history coordi- 
nate with all other subjects taken together, and 
chemistry might seem to be subordinate to history. It 
is desirable, usually, that the classification shall put 
coordinate classes on the same plane, and this the 
dichotomous division cannot do. 

Moreover, this sort of division embodies very little 
information ; it points out a class which has a certain 
character and another which lacks it ; the latter is de- 
scribed in negative terms only. The other type of 
classification presents a number of classes, each de- 
scribed in terms of some positive quality. Still there 
are many cases in which interest centers in those mem- 
bers of a class which possess (or lack) some certain 
character. For some purposes the division of popula- 
tion into voters and non-voters, or into literate and 
illiterate, may be quite as satisfactory as any other. 

Sometimes our information regarding a class is so 
imperfect that a dichotomous division is the only one 
we can use. In a given shipload of immigrants we 
might know that some were Italians, and know nothing 



40 CLASSIFICATION 

about the nationality of the rest except that they were 
not Italians. Or it might be that those outside the 
class positively characterized had so little in common 
that no class or series of classes, coordinate with the 
first, could include them all: the chemist's division of 
elements into metals and non-metals illustrates this. 

It has often been said that a dichotomous division is 
the only one which insures against the omission of any 
individual. Every member of a class must either pos- 
sess a certain quality or be without it ; all that are ex- 
cluded from the first class are necessarily included in 
the second, while in the other sort of division it is easy 
to overlook something. But if many classes are to be 
included, the dichotomous division soon becomes almost 
unmanageable, and if it is not carried out to the end 
we will not discover every class, although all are for- 
mally included. If it is carried out exhaustively, every- 
thing will of course be identified ; but the same would 
be true of any other type of classification. Jevons 
holds that diagnostic classifications should usually be 
dichotomous. 

Requirements of Classification. — In any scientific 
classification (1) the sub-classes must include all that 
is included in the main class; and (2) they must not 
overlap, i. e,, no individual should belong to two classes 
at once. To classify people as large and small would 
violate the first of these rules, while to classify them as 
large, small, and blue-eyed, would violate both. Viola- 
tion of the first rule results in incomplete division ; 
violation of the second, in cross-division. 

Incomplete division is a consequence of failure to 
carry out a division to the end ; sometimes the principle 



FAULTY CLASSIFICATION 41 

of division does not seem to permit this, or some of the 
data included may be of so peculiar a character that 
they do not seem to fall into any well-marked classes. 
An escape from difficulties is sometimes found in a 
miscellaneous class, which shall include all cases not 
otherwise provided for. When this is employed, the 
classification is certain to include all cases. The mis- 
cellaneous class corresponds to the negative class in 
dichotomous division. 

Cross-division is a consequence of employing more 
than one fundamentum divisionis. In the example 
above, both size and eye-color were employed as bases 
of division. 

Every classification should be complete or exhaustive ; 
it should provide a place for every item. But a sort of 
cross-division may sometimes be very useful, as in index 
or diagnostic classifications. Ordinary subject indexes, 
classification of books under author and subject, or of 
college courses under department and year, are cases 
in point, as is also the classification of a disease under 
each of its several symptoms. 

A class which is divided into sub-classes is technically 
called a genus; while each of the sub-classes is a species, 
" Caucasian " is a species of the genus " man.'' If a 
sub-class were to be divided it would be a genus in rela- 
tion to its sub-classes : Slavs are a species of the genus 
Caucasian. Any class, then, regarded as inclusive of 
other classes is a genus, whereas if it is regarded as 
subordinate to some higher class it is a species, A 
class which is so wide that no other can contain it is 
called a summum genus or highest genus ; it alone can 
never be a species. A class which includes so little that 



42 CLASSIFICATION 

it can not be subdivided is an infima species or lowest 
species ; it can never become a genus. 

An individual which is so unique that it can be in- 
cluded in no class whatever is sui generis. 

Under ordinary conditions there is little use for these 
last three terms. It may be doubted whether there is 
such a thing as an individual thing sui generis, and 
whether there can be more than one summum genus, or 
any inflma species which is not a class of one member 
only. In any given investigation they may be employed 
in a relative sense. For anthropology, mammal might 
be regarded as the summum genus; and an individual 
whose peculiarities defy all attempts at classification on 
usual lines might be spoken of as sui generis; a species 
which could not usefully be divided might be regarded 
as an infima species. But this use of the terms would 
not be entirely accurate. 

The use of genus and species as described above is 
the traditional logical usage ; but in the biological sci- 
ences they are used in a different sense. In those sci- 
ences the terms are not relative ; a class is not a species 
at one time and a genus at another. Homo is always a 
genus ; formerly it was thought to have two species, 
man and the chimpanzee, but now man, homo sapiens, 
is regarded as the only species in the genus. The Cau- 
casian race is a variety under the species, homo sapiens. 
Homo is included in the order, primates, etc. 

EXERCISES 

1. What is classification? 

2. What is an Index-classification,^ What is its purpose 



EXERCISES 43 

and on what sort of quality is it based? How would you 
construct an Index-classification of the rulers of Europe 
during the Nineteenth Century? 

3. What is a Diagnostic-classification? State its purpose 
and its principles. How would you construct a classifica- 
tion which would serve for the identification of birds? 

4. What is the purpose of classification as used in scien- 
tific work? What is the difference between an artificial 
and a natural classification? 

5. What is a Dichotomous Division^ and what are its 
strong and weak points ? Make a dichotomous division of 
educational institutions. What is a cross-division? How 
is it caused^ and when may it be useful ? Give examples of 
a genus^ a species^ a summum genus, an infima species, a 
thing sui generis. Contrast the biologist's use of '' genus '* 
and *' species " with the more general logical usage. 

6. Criticise the following classifications and divisions: 
a Men may be classified as white and colored. 

h Trees^ as fruit-trees^ shade-trees and forest-trees. 

c The fine arts^ as sculpture^ paintings drawing, 
architecture, poetry and photography. (Fowler.) 

d Books, as those on history, science, poetry, religion 
and belles-lettres. 

e Political parties, as conservative and radical. 

/ The states of New England, as Maine, New Hamp- 
shire, Vermont, and Connecticut. 

g Mind, into intellect, feeling and will. 

h Body, into extension, weight, resistance, etc. (Mel- 
lone.) 

i Religious, into monotheistic and polytheistic. 

j Americans, into white, black and foreign-born. 

h Politicians, into honest and dishonest. 

I Books, into dull and interesting. 
m Games, into those which are athletic and those which 
are intellectual. 

n Pictures, into paintings, engravings, posters and pen 
and ink sketches. 

o Domestic animals, into those which are useful and 
those which are pets. 

p Motion, into molecular and molar. 

q Bodies, into light, heavy, and dense. 



44 CLASSIFICATION 

r Men^ into those whose main pre-occupation is to get 
through time and those whose aim it is to find 
time for all that has to be got through. 
Can you state circumstances in which any of the above 
might be useful and satisfactory? 

7. Divide and sub-divide: Propositions^ Athletic sports^ 
College publications^, Government^ Poetry^ Furniture_, Ilaces_, 
Schools. 

8. Criticise the classing together of negroes^ coal^ and 
black chalk on the ground that they are similar in being 
blacky solid, extended, divisible, heavy, etc. (MeLlone.) 



CHAPTER IV 
THE USE AND MISUSE OF WORDS 

Discrimination, Conception, Abstraction. — It will be 
remembered that a thing is put into a given class by 
virtue of its possession of some quality or relation, a 
class being simply a group of things which have in 
common one or more qualities or relations. Any given 
thing might, therefore, be classified in several different 
ways. Bucephalus, for example, might be classified as 
a horse, or as a colored object, or as a consumer of 
hay, or as a possession of Alexander the Great, and so 
on. Indeed, most concrete objects might be classified 
in hundreds of ways. For every characteristic which a 
thing possesses there may be a class, and the way in 
which we shall classify it in any given instance will 
depend upon the purpose we have in view. For his 
teacher the small boy is a pupil ; for the cat, a source 
of danger,, and so on. And each mode of classification 
is correct in its place. 

But before an object can be classified in a given way 
it is, of course, necessary to note what qualities it does 
possess. Ordinarily we note very few of these. Most 
of us see only the most obvious and striking qualities of 
things, and we often see those very imperfectly. We 
get a vague general impression and fail to analyse it 
into its elements. The child, in his earliest experiences, 
hardly discriminates the different qualities of a thing 
at all, for his first experiences are very much confused, 

45 



46 THE USE AND MISUSE OF WORDS 

We know things only as we know their quahties and 
relations, and the better we can distinguish and relate 
these the better we know the object. Analysis of the 
concrete datum is presupposed in classification and in 
all the other higher manifestations of consciousness. 

When we analyse a thing we pick out its various ele- 
ments and think of them as more or less isolated from 
the complex in which they were perceived. We can 
think of greenness or roundness without thinking of 
size or hardness or of any of the other qualities with 
which greenness or hardness always occurs. We never 
perceive greenness or hardness by themselves, but we 
can think of them without taking into account the other 
qualities. The mental act whereby we think of them in 
that way cannot be perception ; nor can it be memory, 
for memory, like perception, is of concrete complex 
things, whereas these qualities are simple and abstract. 
The mental act in which we bring before ourselves a 
simple quality is conception; and the thought of the 
quality is a concept. We have concepts of abstract 
qualities, but we cannot have percepts of them. But 
we may also have concepts of concrete things. Our 
idea of some particular horse, say Bucephalus, is not 
a memory, nor is it a perception; it is a concept.-^ We 
may also have concepts of things which we have per- 
ceived; indeed, every perception involves conception as 
well. We are immediately aware of certain qualities, 
but, more than that, we have an idea of a complex whole 
possessing more or less coherence, permanence, etc. 
Whenever we think of a class of objects, qualities, or 

1 Both Concept and Conception are used for the idea of the 
thing or quality, 



CONCEPTS 47 

what not, we do so by means of conception. The 
thought of anything is a concept. Some concepts are 
universal, some are particular ; some are concrete, some 
are abstract ; some are of real things, some of imaginary 
things, and so on. Everything that is thought of is 
thought of in a concept, or rather, the thought of any- 
thing is a concept of that thing. 

In conceiving anything two elements are present: 
the symbol, and its meaning. In the concept " horse " 
the symbol is the word " horse " ; the meaning is the 
sum-total of qualities which that word implies or the 
objects to which it may be applied. The symbol is not 
necessarily a word : we might think of horses without 
having in mind the word. The mental picture of a 
horse might be the symbol. If we were trying to con- 
vey the idea of a horse to a person who did not under- 
stand English, we might use a drawing or imitate the 
sound of galloping, and so on. In all these cases the 
meaning would be the same, though the symbol would 
not. The essential element in the concept is the mean- 
ing ; so long as that remains the same we have the 
same concept, no matter what the symbol. The same 
thoughts may be present in two minds, one of which 
thinks in English and the other in German, or one of 
which thinks in words and the other in mental pictures. 
The superiority of words as symbols will be discussed 
presently. 

It is customary to treat logic as if it dealt solely 
with concepts, judgments and inferences; but in treat- 
ing logic as a part of scientific method, as a part of 
the science of getting knowledge, it will be well to con- 
tinue to speak as if we were dealing directly with the 



48 THE USE AND MISUSE OF WORDS 

facts and not with mental counters. In other words, 
logic may be regarded as a science of things as well as 
a science of thoughts. It deals, it is true, only with 
the most general aspects of things ; not with their spe- 
cial qualities, as do the special sciences, such as physics, 
etc. It has to do with that which is common to 
all fields of facts. In certain cases it may be more 
convenient to speak of the concepts rather than of the 
things conceived, as, for example, in geometry, where 
the things conceived are certain highly abstract rela- 
tions and the like; but even in such cases the other way 
of speaking would be possible. 

Necessity for Language. — Mention has already been 
made of the necessity for describing or in some way 
representing the things we know. The means most uni- 
versally employed and most completely developed is, of 
course, language. A language, from the point of view 
of logic and scientific method, is simply a highly com- ' 
plex system of symbols for the representation of all 
kinds of objects and experiences, of the conclusions 
and constructions based upon experience, of laAvs, and 
so on. Language, as already noted, is a condition of 
all progress beyond the merest rudiments of knowl- 
edge. It might seem to be of no use in the field of 
observation, but an observation made for some special 
purpose or under experimental conditions implies a 
previous statement or representation of the thing to be 
observed. Memory includes a representation of past 
experience by means either of a mental picture or of 
some other sort of symbol, such as the name of the 
thing. All spoken and written evidence, of course, im- 
plies language ; and inference involves the statement to 



LANGUAGE 49 

ourselves of a conclusion from something observed or 
thought of. Classification obviously requires the use 
of symbols.^ So important is language for the work 
of thinking that logic has sometimes been defined as 
a branch of the study of language. Whately said that 
" Logic is entirely conversant about language." Some 
have maintained that all growth in thought has fol- 
lowed the development of language and would have 
been impossible without it ; in other words, that lan- 
guage always precedes thought ; that man is intelligent 
because he has language and not vice versa. These 
may be extreme views, but it is certain that systematic 
knowledge cannot go far without a coherent system of 
symbols, and that language is infinitely superior to all 
other kinds of symbols.^ Any examination of the 
processes by which knowledge is attained must give 
careful attention to the consideration of language. 

If language were perfect, it would not be necessary 
to discuss it at any length in this connection, but its 
imperfections are such as to lead very often to mistaken 
ideas and wrong conclusions. It will be necessary, 
therefore, to examine language in order to discover 
these imperfections and the means of avoiding them. 

Terms. — A word or group of words stands as the 
representative of some thing, quality, relation, action, 

2 Sometimes the mental picture of an individual may stand for 
the class ; the image of a tree may stand for the class tree^ but 
when we know the name of the class or kind, we usually represent 
the class to ourselves by means of the name. Mental pictures are 
liable to vagueness and to modification, and it has been shown that 
scientists, for example, tend to represent things to themselves 
almost exclusively by means of words, particularly as they advance 
in years. 

3 For a discussion of this question see Stout, Manual of Psy- 
chology, chap. v. 



50 THE USE AND MISUSE OF WORDS 

idea, and so on, or some group or combination of them. 
Such a word or group of words is called a term, A 
term might consist of any number of words and con- 
tain various subordinate clauses, but if it stood as the 
symbol of some single object of thought it would still 
be one term. " Man '' and " The torch in the hand of 
the Statue of Liberty in New York Harbor " are 
equally terms, for each stands for a single object of 
thought. The inevitable difficulties with regard to the 
use of terms arise from the fact that a word or a 
group of words may stand for more than one thing ; 
it may have a variety of meanings and is therefore liable 
to misinterpretation. Most words are used in more 
senses than one, so the danger of confusion is always 
present. There are several causes for this multiplica- 
tion of meanings. One of the most important is (1) the 
tendency to use a word in a sense wider than the one in 
which it was formerly used, to use it more generally, to 
generalize it. Lens meant originally only a double con- 
vex piece of glass ; such words as curve, acid, metal, 
salt, etc., illustrate this tendency. 

There is also (2) a contrary tendency to limit the ap- 
plication of words, to use a term in a narrower sense 
than formerly, a tendency toward specialization. 
Minister meant originally a servant; now it means, 
among other things, the highest representative of a* 
state, one of the most exalted " servants " of a govern- 
ment. " Deacon, bishop, clerk, queen, captain, general, 
are all words which have undergone a like process of 
specialization. In such words as telegraph, rail, signal, 
station, and many other words arising from new inven- 
tions, we may trace the progress of change in a life- 



SPECIALIZATION OF TERMS 51 

time." The use of Congressman to describe Repre- 
sentatives only, and of Protection as a name for 
an economic policy, are further illustrations of the 
process. 

These tendencies may affect a word and its deriva- 
tives in different degrees and different directions. Com- 
pare, for example, distinguish and distinguished; 
dissolve, dissolute and dissolution; matter and material- 
istic; respond and responsible; design, designer and de- 
signing, etc. The popular and the technical uses of a 
term are usually different, one being broader or nar- 
rower than the other ; phenomenon, sensation, idea, are 
illustrations. Sometimes a special use of a word is only 
local, as in dialects, or for a short space of time, as in 
slang. 

In addition to these tendencies to generalize and to 
specialize the meaning of terms there is (3) another 
by which there is a transfer of meaning to associated 
objects or to those which are analogous.* The use of 
the word church to designate a religious society, or of 
chair to indicate a presiding officer, or of bench to 
stand for the judiciary, are illustrations of the trans- 
fer of meaning to associated objects, and such expres- 
sions as a dull student, a hard examination, a brilliant 
game, etc., illustrate the transfer to analogous objects. 

There are (4) some other cases of less importance: 
sometimes two words which were originally different and 
of different derivations are alike in sound and spelling 
and might possibly be mistaken for each other ; such 
as, mean in the sense of middle and mean in the sense 
of low; pound :n the sense of weight and pound meaning 
a pen, pen as an inclosure and pen as an instrument of 



52 THE USE AND MISUSE OF WORDS 

writing, etc. Sometimes words are alike in sound but 
different in spelling, as right, wright and rite, or rain 
and reign; in other cases they are alike in spelling but 
different in sound, as lead, the metal, and lead, some- 
thing to be followed, etc.^ These last three cases are 
of little importance since the confusions resulting are 
usually of only momentary duration. In the first three 
cases, those of generalization, specialization and trans- 
fer of meaning, the confusion results from the con- 
tinued use of a word in the older sense after its meaning 
has been extended to a new field. 

If the various meanings are clearly distinguished and 
widely separate, the context will usually make clear 
which is intended ; but the meanings are most frequently 
very similar or closely connected, otherwise the same 
word would never have been used for both. The serious 
consequences of these confusions are seen in the fact 
that so many disputes and differences of opinion result 
from a difference in the use of terms. 

Kinds of Terms. — 1. Singular and General. — ^We 
have discussed the causes of ambiguity in terms ; it will 
be well to examine some of the different kinds of terms 
in order to discover just what sorts of confusion are 
likely to be found. There are some words, such as 
proper names, which would not seem liable to ambi- 
guity since they usually have little or no meaning; but 
after all there may be uncertainty enough with regard 
to the application of the name, as every case, of mis- 
taken identity shows. 

Proper names are simply one variety of individual 

4 Most of the illustrations used in the two pages above have 
been taken from Jevons, Lesson in Logic, 



SINGULAR AND GENERAL TERMS 53 

or SINGULAR terms. " The first president of the United 
States " is quite as definite in its apphcation as any 
proper name could be. A singular term is a term which 
can be applied, in a given sense, to one single, indi- 
vidual object only. On the other hand there are terms 
which may be applied in the same sense to an indefinite 
number of objects. Man, president, book, college, etc., 
are general terms. A term which was originally sin- 
gular may become general, as illustrated in the expres- 
sions, " A Daniel come to judgment," " A Homer," " A 
Hannibal," etc. On the other hand singular terms 
may be so combined as to apply to only one individual ; 
the first president, the wisest man in the world, the 
longest river, the highest mountain, etc., are such 
cases. 

The chief difficulty in the case of singular terms is 
the liability to error with regard to the individual to 
whom the name applies. The form or the context usu- 
ally shows clearly enough whether a term is singular 
or general. ^ 

In the case of general terms there is much more diffi- 
culty: in the first place the meaning may be vague; 
the application of the term may not be definite ; in the 
case of such words as rich and poor, wise and ignorant, 
and a great many others, there is no universal agree- 
ment and there is seldom a definite notion as to the 
range of application in any particular case. Again, 
where the term has a plurality of applications, each of 
which may be sufficiently definite, the wrong one may be 
employed or understood in any given case. The word 
lam, for example, means, in one field, a prescribed rule 
of action, something imposed from without and having 



"i 



54 THE USE AND MISUSE OF WORDS 

a binding force, as a civil law. In the natural sciences, 
on the other hand, a law is simply a statement of the 
way in which things do invariably behave. Obviously, 
one who carries over into the consideration of natural 
phenomena the conception of law employed in legal 
practice, is liable to have a very mistaken view of 
Nature. There is a multitude of terms in which such 
differences are to be found. The Latin lex meant origi- 
nally something fixed or set, so both these meanings 
might be regarded as specializations in different direc- 
tions of the original meanings. In other cases one 
meaning is obviously more or less general than the 
other. In the commandment, " Thou shalt not kill," 
the word Mil is obviously less general than is the state- 
ment, " To kill is to deprive of life " ; or again, the 
words rest, sleep, etc., are not intended to cover all 
possible cases in the statement, " Rest, food and sleep 
are necessary to life." Any mistake as to the exact 
sense in which a word is used will be certain to lead to 
mistaken opinions. • 

2. Concrete and Abstract Terms. — This brings 
us to the distinction between concrete and abstract 
terms, or between terms used in an abstract sense and 
the same terms as used in a concrete sense. 

An abstract term, as the name implies, stands for 
something which is the product of abstraction ; it is 
something separated from its context and considered by 
itself. For example, qualities are known only as they 
occur in an object, in a complex something which in- 
cludes many other qualities. We have already seen that 
these qualities are not recognized as separate things in 
the child's earliest experience. 



ABSTRACT TERMS 55 

If a quality always appeared in the same setting, it 
would never be discriminated and hence could never be 
abstracted. To quote Professor James's illustration, 
if all wet things were cold and all cold things were 
wet, we should never distinguish coldness from wet- 
ness. But most qualities do occur in a variety of set- 
tings and can therefore be discriminated and abstracted. 
When a quality is abstracted it can be treated, for cer- 
tain purposes, as a separate thing. In studying color, 
we disregard the other properties of colored objects 
and treat their colors as something independent. 

There are many degrees of abstraction : blue is ab- 
stract as related to a blue object, but comparatively 
concrete as related to color. An abstract term may be 
the name of a relation, as height, or an action, as 
walking, or of any characteristic whatever, abstracted 
from its setting and regarded as an independent thing. 
The word which stands for this characteristic will be 
an abstract term. A given term is often used in both 
senses : in the sentence, " Government is necessary to 
civilization," the term government is said to be used in 
an abstract sense ; in the sentence, " This government is 
a republic," it is concrete. To confuse the more general 
with the less general meaning of a term or the abstract 
with the concrete use of it, or to argue from a term 
taken without qualification to the same term qualified 
in some particular way, is to' commit a fallacy, the 
Fallacy of Accident, To conclude that it would be 
meritorious to give a beggar a dollar because charity 
is a virtue would be to commit this fallacy. To con- 
clude that, because the only Filipinos you have seen are 
small, a Filipino is a small person, would be to commit 



56 THE USE AND MISUSE OF WORDS 

what is sometimes called the Converse Fallacy of Acci- 
dent; in this, we argue from the concrete or the less 
general or what is true in particular circumstances, to 
the abstract or the more general or to what is true 
apart from particular circumstances. 

The ancient example, " What is bought in the mar- 
ket is eaten ; raw meat is bought in the market ; there- 
fore raw meat is eaten," illustrates the simple fallacy 
of Accident. So also does the following : " The Greeks 
produced masterpieces of art, and as the Spartans were 
Greeks, they produced masterpieces of art." (Davis.) 
" Greeks," in the major premise, is used in the generic 
sense. In the minor, it has a more specific meaning. 

To argue that strychnine should be freely sold be- 
cause it is very useful (as a medicine) would be to com- 
mit the converse fallacy. 

3. Collective and Distributive Terms. — Another 
distinction which is of great importance in dealing with 
terms is that between collective and distributive terms. 
Army, for example, is a collective term; it stands for 
a number of individuals taken together in a group ; it 
is a group term. A term like man, on the other hand, 
has no such significance. It applies equally to any and 
every individual in a class. In an expression like all 
men, for example, there is danger of confusion ; it 
might be taken to mean all taken together, as in " All 
living men number about 1,500,000,000"; or it might 
be used distributively, as in " All men are mortal." 
Synonyms of the terms collective and distributive are 
jointly and severally. Obligations are sometimes laid 
upon individuals which they are bound jointly or sev- 
erally to observe. 



COMPOSITION AND DIVISION 57 

Confusion between the collective and the distributive 
uses of a term leads to the Fallacies of Composition and 
Division; arguing from the distributive to the collec- 
tive use results in the fallacy of Composition. " Each 
member of the committee is insufficiently informed, 
therefore the committee as a whole is not sufficiently 
informed," contains a fallacy of Composition. But to 
argue that because a navy as a whole was weak, the 
individual ships were therefore weak, would be to com- 
mit a fallacy of Division. These fallacies should be 
kept clearly distinct from the fallacy of Accident. Here 
we are dealing with a group ; the question is, are we 
dealing with it simply as a group, or are we thinking 
of the individuals of which it is made up? In the other 
case we were not concerned with a group at all. 

4. Other Kinds of Terms. — Various other distinc- 
tions might be made among terms ; there is, for ex- 
ample, a distinction between positive and negative 
terms ; the former being those which imply the presence, 
and the latter those which imply the absence, of a qual- 
ity. White, just, warm, etc., illustrate the former; 
blind, empty, unconscious, the latter. There is little 
danger of confusion in this and in most of the other 
cases which might be included, so we will pursue them 
no further. 

Definition. — ^In any case in which misunderstanding 
is likely to occur, the first thing to do is, obviously, to 
make clear what it is that the term stands for. In the 
case of a proper name the application of the term could 
be shown by producing, or pointing out, or describing, 
the individual thing for which it stands, and so of other 
singular terms. But with general terms that is not 



58 THE USE AND MISUSE OF WORDS 

possible ; a general term stands for all possible cases 
of a given sort, past, present and to come, and any 
example or series of examples could at most illustrate 
the meaning of the term. Sometimes an example will 
show clearly enough, for ordinary purposes, what is 
meant. But any example might illustrate a variety of 
things ; if two persons, each of whom was entirely un- 
acquainted with the language of the other, should try 
to communicate by pointing to objects to indicate the 
meaning of the words they were using, they would illus- 
trate the uncertainty of this method in its extreme form. 
If one of them should point to a horse, he might mean 
any one of a dozen different things : horse, or simply 
animal, or useful animal, or large object, or gray, or 
beautiful, or dangerous, and so on. In a minor degree 
that sort of difficulty is always present when illustra- 
tions are employed to indicate the meaning of terms, 
and the method of illustrations is never entirely satis- 
factory. 

In Plato's Euthyphro Socrates asks Euthyphro, who 
claims to have a precise knowledge of the subject, 
"What is piety and what is impiety? " The reply is, 
"Piety is doing as I am doing; that is to say, prose- 
cuting any one who is guilty of murder, sacrilege, or of 
any other crime — whether he be your father or mother 
or some other person, that makes no difference ; — and 
not prosecuting them is impiety." But Socrates is not 
satisfied with this. " Remember,'' he says, " that I did 
not ask you to give me two or three examples of piety, 
but to explain the general idea which makes all pious 
things to be pious." In other words, what quality must 
things possess in order to be called pious .^ When we 



THE MEANING OF TERMS 59 

ask for a definition of a term we wish to know what 
qualities a thing must have in order to make the term 
appUcable. 

It should be noted that nearly all terms have two 
aspects : they stand for objects and they imply the 
qualities which those objects possess. The term man 
stands for any or all individual men, past, present and 
to come. It also implies all the qualities which a being 
must possess in order to be included in the class. In 
the case of a general term it is obvious that all the in- 
dividuals for which it stands — in technical language, 
its total extension — could never be presented. The only 
way of indicating the full extent of its application is 
to show what qualities it implies, to tell what its inten- 
sion is. That might conceivably be done by enumerat- 
ing all the qualities which were regarded as essential. 
If things in a given group were so unique that they 
could not be included in a larger class, enumeration of 
their qualities would be the only way of showing what 
they were. But in all ordinary circumstances, this proc- 
ess can be abbreviated by stating (1) the class to which 
the things belong and (2) the quality which distin- 
o-uishes them from the other members of the class. ^ 
The class-name will obviously imply the presence of 



5 " Definition " has been variously defined. " Given any set of 
notions, a term is definable by means of these notions when, and 
only when, it is the only term having to certain of these notions 
a certain relation which itself is one of the said notions." (Rus- 
sell, The Principles of Mathematics, Vol. I, chap, xi, sec. 108.) 
A term is defined by being given a place in a set of notions, which 
place can be occupied by it and by it alone. Instead of being 
assigned to a class it is given its place in a complex system of 
concepts. This last might be regarded as the more complete form 
of definition, whereas the former, the traditional form, is less 
complete, though adequate for ordinary purposes. 



60 THE USE AND MISUSE OF WORDS 

the qualities which these things have in common with 
the others in the class. 

The class which includes a thing is its genus: ^^ plane 
figure '' is the genus of " triangle." And the quality 
which distinguishes it from the other members of the 
class is its differentia or ^peculiar prop^.rty ; " three- 
sided " is the differentia of " triangle.'' A property is 
any essential quality : having an equal number of sides 
and angles would be a property of " triangle." An 
accident is a quality which may or may not be present 
in any or all members of a group : having a right angle 
is an accident of " triangle." ^ 

Defects of Definitions. — There are several defects to 
which definitions are liable. 

1. They may be too broad, i. e.y they may include 
more than the term is intended to cover. To define a 
square as a rectilinear figure would be a case in point. 
In such definitions the differentia is not given or not 
properly given. 

2. Again, the definition may be too narrow, that is, 
it may exclude part of what the term is intended to 
cover. To define " American citizen " as one born in 
the United States would exclude naturalized citizens. 
In this case an accidental quality is taken as the dif- 
ferentia. 

3. Definitions are sometimes given in obscure or figur- 
ative or ambiguous language. Dr. Johnson's defini- 
tion of a network as " anything decussated or reticu- 
lated with interstices between the intersections " is a 

6 These four terms, germs, differentia, property and accident, 
together with species, are what have been traditionally known in 
logic as the five Heads of Predicables or the five ways in which 
a predicate may be affirmed of a subject. 



DEFINITION 61 

favorite Illustration of the obscure definition, the defini- 
tion of ignotum per ignotius, Spencer's definition of 
evolution as " an integration of matter and a concom- 
mitant dissipation of motion ; during which the matter 
passes from an indefinite incoherent homogeneity to a 
definite coherent heterogeneity; and during which the 
retained motion undergoes a parallel transformation," 
is sometimes charged with this fault. It should be re- 
membered, however, that when a term is to be used with 
scientific exactness it may be necessary to couch its 
definition in very technical terms ; to one who had read 
the discussions which lead up to it, Spencer's definition 
would not seem obscure. Figurative and ambiguous 
language should always be avoided when exactness is 
the aim. Such language may give some suggestion of 
the meaning of a term, but does not really define it. 

4. Sometimes unessential attributes are employed 
in defining a term: e, g,^ " Books are the things out of 
which libraries are made." Such definitions are obvi- 
ousl}^ faulty. They use an accident as the differentia 
and do not give the meaning of the term. 

5. Whenever it -is possible, a definition should be 
stated in positive rather than negative terms ; to define 
" an under-classman " as " a student who is not an up- 
per-classman " is to tell what he is not instead of telling 
what he is. 

6. Another sort of bad definition is one in which the 
definition contains the term to be defined or some syno- 
nym or exact correlative of it. " Life Is that which 
distinguishes living from non-living things " would be 
a flagrant case ; " A cause Is that which produces an 
effect " is little better." A definition should state clearly 



62 THE USE AND MISUSE OF WORDS 

the exact meaning of the term to be defined. There are 
cases, however, where a complete definition is not neces- 
sary. Where the hearer is in doubt which of two well- 
known meanings is intended, or where the term is al- 
ready familiar but is used with a slightly different 
shade of meaning, in other words, where the genus is 
already known, the briefest indication of the differentia 
may suffice ; sometimes the mention of any accidental 
quality, or even the use of an illustration, may be 
sufficient. , 

EXERCISES 

1. Make a list of ten words which are sometimes misused 
through the fact that they have undergone generalization; 
a similar list of those which have undergone specialization; 
a list of five in which there has been a transfer of mean- 
ing to arralagous objects. 

2. Bring ten examples of singular terms and ten of 
general terms; ^ve of general terms which were originally 
singular or were derived from singular terms. 

3. Give ten examples of collective terms and ten of dis- 
tributive. Show how error might arise in this connection. 

4. What is a definition? Compare definition and de- 
scription. Define the following terms: Book^ Party^ Col- 
lege^ Republican, Honesty^ Foot-ball^ Dormitory, College- 
spirit, Club, Money, Success^ Trustee, Tariff^ Saint, Geo- 
metrical figure. 

5. Criticise the following definitions: 

(1) A phonograph is a mechanism lor recording and 

reproducing sounds. 

(2) A sea is a body of water, next in size to the 

oceans, entirely, or almost entirely, surrounded 
by land. 

(3) A library is a collection of books generally for 

personal use and not meant for merchandise. 

(4) A wagon is a conveyance mounted on wheels and 

drawn by some animal^ usually a horse. 



EXERCISES 63 

(5) Oxygen is the most important gaseous element 

known^ without which combustion and animal 
life would be impossible. 

(6) A sensation is a modification of consciousness 

produced by the excitation of a cortical cen- 
ter through the agency of an afferent nerve- 
current. 

(7) *' Life is a continuous adjustment of internal to 

external relations." 

(8) Logic is the Baedeker of the world of thought. 

(9) A cause is that w^hich produces an effect. 

(10) A book is a combination of leaves and cover. 

(11) A sun-dial is an affair for telling time by means 

of the sun. 

(12) Public opinion is the opinion of people gen- 

erally. 

(13) A student is one whose principal business is 

study. 

(14) A just judge is one who never shows partiality 

in his decisions. 

(15) Wood is the ligneous part of trees. 

(16) Football is a game which is usually played in 

AAierica with a large ball in the shape of 
an oblate spheroid^ whereas in England a 
spherical ball is used. 

(17) A liar is a man who wilfully misplaces his onto- 

logical predicates. 

(18) A philosophical work is one which treats of some 

metaphysical subject. 

(19) A philosophical work is one which deals with 

something abstract and difficult. 

(20) A false weight is an abomination. 

(21) The quality of a proposition is what tells us 

whether it is affirmative or negative. 

(22) Definition is telling what a word means. 

(23) A religion is that which satisfies the highest 

needs of man. 

(24) Matter is the stuff out of which things are 

made. 
6. What fallacies are committed in the following cases .^ 






64 THE USE AND MISUSE OF WORDS 

(1) The holder of some shares in a lottery is sure 

to gain a prize^ and as I am the holder of some 
shares in a lottery I am sure to gain a prize. 
(Hyslop.) 

(2) A monopoly of the sugar-refining business is 

beneficial to the sugar-refiners ^ and of the corn 
trade to the corn growers; and of silk-manu- 
facture to the silk weavers; and of labor to 
the laborers. Now all these classes of men 
make up the whole community. Therefore a 
system of restrictions upon competition is 
beneficial to the community. (Hyslop.) 

(3) Who is most hungry eats most; who eats least 
is most hungry; therefore who eats least eats 
most. 

(4) All the trees in the field make a dense shade; 
therefore this elm tree^ which is one of them^ 
makes a thick shade. 

(5) Cities are governed by mayors; hence a mayor 
was the highest official in ancient Rome. 

'(6) The major received a D.S.O. for attacking the 
enemy and appropriating their supplies ; there- 
fore it is praiseworthy to steal. 
^^(7) The Irish are quick-witted; hence that Irish 
policeman must be quick-witted. 

(8) This ship is one of the best in the worlds for it 
belongs to the British Navy^ which is the best 
in the world. 

(9) Americans are liberal; hence this man may be 
counted on to give liberally, since he is an 
American. 

(10) We can now see the results of giving the Jiegro 
all the rights and privileges of the white man. 
Two months after he was placed in office, this 
colored man absconded with all the funds un- 
der his control. 

(11) Every man has a right to teach his religious bc" 
liefs; therefore it is not out of place for a 
college instructor to do so in the discharge of 
his duties. 



EXERCISES 65 

(12) Any student in college would stand higher in his 

class if he received higher marks; hence if all 
marks were raised 10% every man would 
stand nearer the head of his class. 

(13) Pine wood is good for lumber; matches are pine 

wood; therefore matches are good for lumber. 
(Hyslop.) 

(14) To teach a child is to improve him; showing him 

how to pick pockets is teaching him; hence 
that improves him. 

(15) Poisons cause death; nux vomica is a poison; 

therefore it causes death. 

(16) This reformer was working for selfish ends all 

the time ; no more reformers for me. 

(17) Since attending that socialist meeting I have 

had no confidence in socialistic doctrines. 

(18) He cannot be innocent^ for he was a member of 

the mob which committed the deed. 

(19) Those two horses would make an excellent team, 

for each is the best of its class. 

(20) Five is an odd number; three and two are five; 

and hence each is an odd number. 



CHAPTER V 
PROPOSITIONS 

Difficulties in the use of language are not all pro- 
vided against by the correct definition of terms. Many 
arise in the combination of words into sentences. A 
term, as we have seen, is the representative in lan- 
guage of some object of thought, real or imaginary, 
concrete or abstract. But the mind never rests in the 
contemplation of a single object; it always tends to 
make an assertion or judgment about this object. 
Most logicians are now of the opinion that, even in the 
simplest perception, a judgment is either present or im- 
plied. Introspection will show at once that when we 
hold an object before the mind, there is an inevitable 
tendency to think some assertion about it. The ex- 
pression of this mental assertion or judgment in lan- 
guage is a proposition. 

Kinds of Propositions.' — Propositions are usually 
distinguished according to quality and quantity, (1) 
The qualities are two, affirmative and negative. The 
difference between affirmative and negative propositions 
is sufficiently familiar. It should be remembered, how- 
ever, that the mere occurrence of not or some other 
negative particle in a proposition does not necessarily 
make the proposition negative. The proposition, 
" Those who do not study are in danger of failing," 
is not a negative proposition. It asserts positively 
something about a certain class, namely, " those who 



QUALITY AND QUANTITY 67 

do not study " ; these words constitute a negative term. 
An affirmative statement can be made about a negative 
subject as readily as about any other. In the proposi- 
tion, " Those who do not study are unwise/' the term 
unwise is also negative, but the proposition is affirma- 
tive. To decide whether any proposition is affirma- 
tive or negative, determine whether something is 
affirmed or denied of a subject. What the subject is, 
and what the predicate is, makes no difference ; the only 
question is, do we affirm something or do we deny some- 
thing? (2) With regard to quantity, propositions 
may be either universal or particular, • A universal 
proposition is one which expresses a judgment about 
the whole of the class to which the subject applies. 
" All the stars are suns " is a universal proposition ; so 
is " No planets are self-luminous." (The latter propo- 
sition is negative and denies something of all planets.) 
" Some stars are double " is called a particular propo- 
sition. It asserts something of some individuals of the 
class " stars." By " particular proposition " is not 
meant a statement about some particular individual. 
The proposition " Jupiter is the largest of the 
planets " is not a particular proposition. It is a sin- 
gular proposition, but, since it expresses a judgment 
about the whole of that for which the term " Jupiter " 
stands, it may be treated as a universal proposition. 
The so-called particular propositions are really indefi- 
nite; if the "some" in any proposition meant certain 
particular ones, as it does in certain cases, the propo- 
sition would really be universal ; it would say something 
about all those of whom the assertion was made : as 
" some persons " (meaning A, B, C) " are certain to be 



68 



PROPOSITIONS 



latcc" As used ordinarily, some means certain unspeci- 
fied individuals, it may or may not he all. The word 
indefinite would certainly be more appropriate here, but 
the word particular, with this special meaning, is the 
one which has been used traditionally. 

With this two-fold distinction of quality and quan- 
tity we get four different kinds of propositions : uni- 
versal affirmative, universal negative, particular affirm- 
ative and particular negative. For the affirmative 
propositions the letters A and I are used as symbols, 
A standing for the universal affirmative and I for the 
particular affirmative. E stands for the universal nega- 
tive and O for the particular negative. (These letters 
are from the Latin Affirmo and Nego,) 



r 



Quality 



Propositions ■< 



V 



Quantity 



r 



Universal 



\ 



Particular 



r Affirmative 
I Negative 

Universal 
Particular 
Affirmative A 
Negative E 

r Affirmative I 
I Negative O 



Propositions and Terms. The Relation of Subject 
to Predicate. — The question of the relation of propo- 
sitions and terms is one that naturally arises here. A 
proposition obviously contains terms. Ordinarily it 
is said that a proposition is made up of two terms and 
a copula. One of these terms is the subject and the 
other is the predicate. The copula is that which con- 



SUBJECT AND PREDICATE 69 

nects subject and predicate.: it is always some part of 
the verb to he. Some propositions do not fall natu- 
rally into this form: for example, " The earth moves.'' 
This can, however, be expressed in this form : " The 
earth is a body which moves." 

This form, subject-copula-predicate. Is called the 
" logical form " of the proposition. It often seems 
artificial, but for certain purposes it is convenient to 
employ it, and the attempt to restate propositions in 
this form is an excellent way of finding out just what 
the proposition means. 

The subject of a proposition stands for that about 
which something is said.^ 

The predicate is that which is asserted of the sub- 
ject. The copula is that which connects the two terms 
in a proposition ; but the nature of that connection is 
not always the same. In the propositions, " Aristotle 
was the greatest pupil of Plato," " Aristotle w^as wise," 
" Aristotle was traveling in Asia Minor," and " Aris- 
totle was a philosopher," the copula has, in each case, a 
different meaning. In the first, the relation is that of 

1 A distinction may be made between the grammatical and 
the logical subjects. The grammatical subject is the subject 
of the proposition; it is, as we have seen, a term. The logical 
subject has been variously defined. The definition of the logical 
subject as the subject of the thought seem, on the whole, to be 
the best. (See for discussion, Joseph, Introduction to Logic.) 
The logical subject is that about which the judgment is made. 
For example, in the proposition, " Acid turns blue litmus paper 
red," the grammatical subject is, of course, the word " acid." 
The grammatical predicate is that which stands for what is 
asserted about the subject; in this case, the words "turns blue 
litmus paper red." Changing the proposition into the form of 
subject-copula-predicate, it would read " acid is that which 
turns blue litmus paper red," and the complete predicate would 
be the words following the copula. Now the form of the propo- 
sition may not indicate the real logical subject. If the statement 
just given were the answer to the question, "What can you say 



70 PROPOSITIONS 

Identity; in the second, that of subject and attribute; 
in the third, that of agent and action ; in the fourth, 
that of inclusion of an individual in a class. Logicians 
have usually taken the last of these as . the typical 
relation ; the others can be transformed with more or 
less success into it. The proposition, " Aristotle was 
wise,'' can be put in the form, " Aristotle was a wise 
man " ; and " Aristotle was traveling," etc., can be ex- 
pressed in the form, " Aristotle was a man who was 
traveling," etc. These forms are sometimes criticised 
as not expressing the exact shade of meaning contained 
in the other forms ; but the difference is usually not 
serious, and the performance of certain logical opera- 
tions is much facilitated by so expressing the judg- 
ment as to indicate the inclusion of an individual, or a 
class, in another class. 

In the negative proposition the relation will, of 
course, be that of exclusion. " Minors are not voters " 
indicates the exclusion of the first class from the 

second. 

about acid, the grammatical and logical subjects would cor- 
respond ; but if the question were, " What is the effect of acid 
on litmus paper?" the logical subject (i. e., the thing about 
which the judgment is made) would be that which is expressed 
by the grammatical predicate of the proposition. The form of 
the sentence could be so changed as to make the grammatical 
or verbal subject correspond to the logical subject; in a great 
many cases they do not so correspond. Ordinarily the logical 
subject can be determined only by the context, though sometimes 
it can be indicated by emphasis on certain words. For example, 
"Acid turns blue litmus paper red" would imply, as the subject, 
what is expressed by the words, " the color to which blue litmus 
is turned by acid." Unless otherwise specified the term subject 
will be understood to mean grammatical subject; and 
predicate will mean the term that is joined to the subject by 
the copula. In the treatment of isolated propositions there is no 
occasion for the distinction. It is sometimes said that reality 
as a whole is the logical subject of every judgment. It might 
better be called the ultimate or metaphysical subject. 



DISTRIBUTION 71 

The Distribution of Terms in a Proposition.— There 
are degrees of inclusion and exclusion. In the illus- 
tration just given the whole of the class minors is ex- 
cluded from the whole of the class voters. In the 
proposition, " Some men are not good citizens/' only 
some men or a part of the class men is excluded from 
the class good citizens, but the whole of the class good 
citizens is excluded from that part of the class men 
which is included in the subject. In the proposition, 
" Some men are healthy animals,'' a part of the class 
men is included in the class healthy animals, and conse- 
quently a part of the class healthy animals may be 
included in the class men. Again, in the propo- 
sition, " All men are bipeds," the whole of the class 
men is included in the class bipeds, but so far 
as this proposition informs us, only a part of the class 
bipeds can be included in the class men. When- 
ever, in a proposition, a term is used to indicate 
the whole of the class for which it stands, it is said to 
be distributed; when it covers only a part of the class, 
it is undistributed. The subject of a universal proposi- 
tion is always distributed, because, by definition, a uni- 
versal proposition is one which asserts something about 
the whole of its subject. It will be seen in the examples 
given above that both the negative propositions dis- 
tribute their predicates. That is always the case with 
negative propositions. They always indicate the en- 
tire exclusion of the predicate from the subject. The 
proposition A, being universal and affirmative^ will dis- 
tribute its subject but not its predicate; J, being par- 
ticular (indefinite) and affirmative, will distribute 
neither; the particular negative, 0, will distribute the 



•72 PROPOSITIONS 

predicate, but not the subject, while the universal nega- 
tive, E, will distribute both subject and predicate. 

Euler's Method. — Euler, a Swiss mathematician of 
the Eighteenth Century, devised the following method 
of representing the relation of subject and predicate 
and the distribution of each. Let each term be repre- 
sented by a circle ; then the E proposition will be rep- 
resented as follows, S standing for the subject and P 

for the predicate: (§)(?)• S and P are shown to be 

entirely excluded from each other; each is distributed. 
The A proposition would be represented in this way: 

/"""^^ S is seen to be entirely included in P, while, so 
» (§)P/ far as we know, only a part of P falls within S ; 

^" — -^^ S is distributed, P is not. In the I proposition 
the circles would overlap. Each would be partially in- 

/^~>; "\ eluded within the other; that is, neither would 
'\jyl_y be distributed. Whether either extended fur- 
ther would be left undetermined; there are four possi- 
bilities, in each of which at least some S is some P. In 

-^^->.^^the O proposition, part of S would be excluded 
\^>iL/ from P ; the rest would be left undetermined; 
while all of P would be outside the specified part of S ; 
S is not distributed, P is. 

The distribution or non-distribution of terms in the 
various propositions may be represented by the follow- 
ing symbols : " - " indicating an affirmative proposi- 
tion, " X " a negative one, and a circle about a term 
the fact that it is distributed.^ 



A, (D-P; E, (S) X (D ; I, S-P; O, S x. ® 

2 The last two of these symbols are adapted from Hyslop, Ele- 
ments of Logic, 



AMBIGUOUS PROPOSITIONS 73 

Ambiguous Propositions. — There are several kinds 
of ambiguous propositions. In the first place the ar- 
rangement of the words and phrases may be such as 
to admit of two interpretations. Familiar examples 
are the prophecy in Shakespeare's Henry F7, " The 
Duke yet lives that Henry shall depose," and the re- 
sponse of the oracle, " Pyrrhus, I say, the Romans shall 
subdue." The expression, " Twice two and three," is 
ambiguous for the same reason, and so is the state- 
ment, " He went away and returned yesterday." In 
the two last, punctuation would, of course, remove the 
ambiguity. Propositions, like " He jests at scars who 
never felt a wound," will sometimes mislead a careless 
reader. Care in the construction of a proposition will 
obviate such difficulties ; where such sentences are 
found, only the context can make clear what the mean- 
ing is. Wrong conclusions in such cases are said to 
result from committing the Fallacy of Amphiboly or 
Amphibology. 

Certain other cases of ambiguity might be brought 
under this heading. One of these is found in the use 
of " all . . . not." In the statement, "All these 
men are not swift-footed," it might be thought that the 
meaning was, " None of these men is swift-footed " ; 
that is, that the subject, these men, was distributed, and 
that the proposition was an E proposition. It is 
usually interpreted as meaning " some are not swift- 
footed," not " all are." It is an E proposition In form, 
but an O proposition in meaning. Again, It might 
seem to imply that " some are swift-footed " ; but this 
last implication is not to be trusted, for we could make 
the original statement if we knew that some of these 



74 PROPOSITIONS 

were not swift without knowing anything about the 
rest. The word somej as already noted, is indefinite ; in 
an affirmative proposition, such as " Some are going,'' 
it seems to imply the corresponding negative, " Some 
are not going," and vice versa ; but these implications 
count for nothing if not confirmed in some other way. 
In interpreting a proposition the only safe rule is to in- 
clude in its meaning only what it must mean, not what 
it may mean. 

In still other cases it is not so much the arrangement 
as it is the character of the terms that occasions diffi- 
culty. Propositions which are introduced by the word 
few are ambiguous. " Few are completely masters of 
themselves " really means that most are not masters of 
themselves, or that not many are. It is an O proposi- 
tion in meaning, though like an I proposition in form. 
It may also seem to suggest the corresponding I propo- 
sition, " Some are masters," etc. The importance of 
making clear the negative force of such a proposition 
may be illustrated thus : suppose we have also the state- 
ment, " All who are masters of themselves are mature 
individuals " ; it might seem that we could conclude 
that few are mature individuals. If the proposition 
*^Few," etc., be put in the negative form given above 
there will be no temptation to draw the erroneous con- 
clusion. Thus in, " Most men are not masters, etc. ; 
those who are, are mature," etc. ; the conclusion, " Most 
men are not mature," does not even seem to follow. 
Professor Hyslop, in his Elements of Logic, calls propo- 
sitions of this sort partitive propositions, because they 
" express a part of a whole of which the implied propo- 
sition is a complementary part." 



PARTITIVE AND EXCLUSIVE 75 

Another sort, similar in certain respects to these, is 
found in the exclusive propositions; they are such as 
have their application determined by such expressions 
as only, alone, none hut, and the like. " None but 
native-born citizens are eligible to the presidency," 
" Only students will be admitted," etc., are exclusive 
propositions. These statements do not mean that all 
native-born citizens are eligible nor that all students 
will be admitted. They are not universal propositions ; 
they do not distribute their subjects. They are equiva- 
lent to the propositions, " Those who are not native- 
born are not eligible," " Those who are not students 
will not be admitted," which are the complementary 
opposites of the original propositions, and are in this 
case E propositions. As the original propositions stand 
they really limit the application of their predicates, 
I, e,, they include the whole of the predicate in the sub- 
ject. Thus they distribute the predicate, in spite of 
the fact that they are affirmative propositions. They 
are, therefore, exceptions to the rule for affirmative 
propositions (p. 71). Another way of restating ex- 
clusive propositions is to convert them, making the 
converse a universal proposition. Thus : " All persons 
eligible to the presidency are native-born citizens " ; 
" All who are to be admitted are college students." 

One other sort of proposition of this general class 
may be mentioned, the exceptive proposition: it is in- 
troduced by such words as " All except," " all but," 
etc. For example : " All but the best will be excluded." 
In addition to the positive statement, a corresponding 
negative is suggested, namely, " The best will not be " ; 
though this last is not certainly true. It is well to re- 



76 PROPOSITIONS 

state such propositions, eliminating the exceptive par- 
ticle. Thus : " All those who are not the best," etc. 

Figurative statements are peculiarly liable to mis- 
interpretation; Hyperbole and metaphor, symbolical 
and allegorical statements, may all be mistaken for 
literal statements, or if recognized as figurative, they 
may be wrongly interpreted on account of the inherent 
vagueness of most figurative expressions. Fallacies 
arising from this cause are known as Fallacies of Figure 
of Speech.^ 

Another source of ambiguity and misinterpretation 
in propositions is to be found in misplaced emphasis. 
Wrong emphasis gives rise to what is known as the 
Fallacy of Accent. To quote from Jevons : " It is cu- 
rious to observe how many and various may be the 
meanings attributable to the same sentence according 
as emphasis is thrown on one word or another. Thus 
the sentence, ' The study of Logic is not supposed to 
communicate the knowledge of many useful facts,' 
may be made to imply that the study of Logic does 
communicate such a knowledge although it is not sup- 
posed to do so ; or that it communicates a knowledge 
of a few useful facts ; or that it communicates a knowl- 
edge of many useless facts. . . . Jeremy Bentham 
was so much afraid of being misled by this fal- 
lacy of accent that he employed a person to read to 
him, as I have heard, who had a peculiarly monotonous 
manner of reading." To introduce italics into a quo- 
tation, with no mention of the fact that they did not 

3 It has been said that some of Locke's erroneous conclusions, 
m his Essay on the Human Understanding, resulted from his own 
use of "the sheet of white paper" as a figure representing the 
mind before experience has begun. 



THE FALLACY OF ACCENT 



77 



occur in the original, is usuall}^ to misrepresent the 
meaning of the original. De Morgan and others have 
pointed out that taking words or passages out of their 
context may have the same consequences. Isolated 
texts from sacred writings are often misused in this 
way ; e. g., " Eat, drink and be merry, for to-morrow 
ye die," " Take no thought for the morrow," etc. 

Quoting an argument which an author has presented 
only in order to refute it<, without mention of his pur- 
pose, is another case of the same sort. 



EXERCISES 

1. In each of the following propositions give (a) the 
complete subject and (b) the complete predicate; (c) re- 
state each in its logical form; (d) give its quantity and 
quality and the letter which symbolizes it. And state 
whether (e) the subject and (f) the predicate are dis- 
tributed. 

1) He laughs best who laughs last. 

2) Few are able to endure such hardships. 

3) Not all who are called are chosen. 

4) Nothing of worth is without honor. 

5) Only genius could have accomplished it. 

6) He little knows you^ who can speak of you in 
such terms. 

) Every bit of success makes further success 
easier. 

8) Like cures like. 

9) There is nothing either good or bad but thinking 
makes it so. 

It is the first step that costs. 

Everything has its limit. 

We demand non-partisan judges. 

His lack of enterprise cost him his position. 

The plowman homeward plods his weary way. 

Contentment is better than riches. 

Every deed returns upon the doer. 



6 

7) All's fair in war. 



78 



riiorosiTioNS 



1 (18) Many :i luoniiiii;- on tlic uioorlaiul have wc lirard 
tlic copses riiigX 
(If)) INM'l'eclioM is bi^yoiul [he reach ol" man. 
Y (^0) My niiiul U) me a. kiiio'doiH is. 
'Sc ^ (!^0 No a(hnission except to ticki't iiohlers. 

yii^ (:2'2) biVery one has the derects of his (]iialili(\s. 
£'(!2.S) Socrati\s taught that no man wouhl knowingly 
(h) wrong. 
(^21) And sihMice, like ii poultice, conies to heal the 

wounds of sound. 
('25) All thi^ world admires heroism. 
{"26) It rains. 



I 



* 



CIIAP'rKR VI 

INDIHIMON 

Generalization and ^A/hat it Involves In the 
two last ('liaf)liM*s wo \\:\\c bron sIikIvIiii;' IIu^ iis(^ of lan- 
^'iiaoo, I lie most ini[)ortant iiislrunuMil of Ihouolit. Wo 
now rolurii lo [\\c coiisidiM'al ion of I ho i'urtluM* [)roo- 
ossos monlloiu^d in our {)rolnninarv siirvi^v of soicMililio 
molliod. ((1ia[). 1.) Obsorvalion aiul olassilioalioii 
liave boon disoussod ahvadv ; il rcMnains lo oxannni* llio 
way in which laws ' oan bo disooviMHul alUM- considorablo 
body of* fac-ls has boon obscM'viul and olassidcHl. Wo 
liavo soon that a. law is a, staliMUiMd of \\\v way in which 
i'acts oi* a, ciM'lain kind bohaM% how I hoy arc lu^lalcHl lo 
other facls, whal aro Iho uni\(M-sal relations in which 
they stand. Our first ({uostion is: IIow :\vc llu^so laws 
su^'g'ostod? What is Iho source of llu^sc^ ocMUMal slalo- 
nionts oi* rolalionshij)? And our siH'ond (|u(\slion is: 
How is a, supposed law to bo established or \ (Milled? 

In answer to the first (|Ui\slion, it may he said that a 
g'onoral statenuMd is usually arriyed at by oHMU^ralizin*;' 
some obsoryed relationship. II* we hayc^ obsiM-Mnl one 
or more instances in which a. cold wild cm* has boon fol- 
lowed by a hot sunnnor, w(^ may ^'onoraliy,(^ tlu^ connec- 
tion and assort that a cold winter is always f'ollowiul by 
a hot sunnnor, that there is an inyariabh^ and iiu^yi table 

1 The previous ohaplia* lias (ioali, in jiart, with iinivcMsal proj>o- 
sitions; the present one is a discussion of the way in Avliieh sueh 
pro})osilions are established. 

79 



so 



INDITCTTON 



(•(intioction between thein. And similarly in any other 
case; A has been followed by B and we conclude that 
cvcrif A is follincrd bif ii, that every A has its B. A 
sino'lo instance may be enough to suu'ii'est a o-oneraHza- 
tion. A o'enerahzation is a universal assertion, not a 
mere attitude of expectation. The lower animals ex- 
hibit a tendency to expect a given thino; when another, 
which has occurred along^ with this, reappears; when 
an animal hears a certain call he may expect food, be- 
cause in the past the two have been connected; when 
he sees a blow descendino; he may expect })aln, and so 
on. lUit to expect a thing- on t]ie recurrence of another 
formerly connected with It, is nof^ttuTsame as to infer a 
universal connection. When I perceive A, I may re- 
member and expect B, without ever having thought of 
a universal relation between the two, without asserting 
that B always follows A. There is no proof that an 
animal can o-onerali/e, that he can thinlc to himself: 
" A call of a certain sort is followed bv food," " A 
blow causes pain,'' and so o\\. He hears the call and 
ex[)ects food, but he does not generalize the connection. 
To do the latter would be ditticult if not impossible, 
Avithout language. This power to generalize, to use 
general a ml abstract ideas, is usually regarded as one 
of the most important differences between human and 
animal intellio'ence. 

Without o'eneralization, our knowled^'e would be con- 
fined to individual facts or to groups of these. We 
have seen that knowledge is not completed by the mere 
accunuilation of observations and the classification of 
what has been observed. The aim of science is usuallv 
said to be the discovery of laws. Now a law, as already 



I 



LAWS 81 

remarked, is the statement of the way in which phe- 
nomena behave, or the way in which they are inevitably 
related to other phenomena. 

This tendency to generalize is, then, a pre-condition 
of all but the most primitive kind of knowledge. But, 
of course, our generalization may not turn out to be a 
law. A law states a universal connection which ac- ^ 
tually holds true, whereas our hasty generalization may 
be entirely unsound. A generalization arrived at in 
the way described above is an inductive inference. An 
inductive inference is a judgment about a whole class 
of facts based upon the observation of individual cases. 
It is a universal conclusion based upon one or more 
particular instances. Obviously, an inductive inference 
must he tested or verified; but before proceeding to the 
discussion of verification it will be well to mention cer- 
tain other terms which are frequently employed in this 
connection. 

Causal Connection. — The terms, cause, causal con- 
nection, causal law, occur constantly in this part of 
scientific method. What is a cause .^ The term implies 
a connection of some sort between phenomena ; but of 
what sort? In ordinary usage it probably means most 
frequently something which produces or brings about 
something else. It has been objected that we can never 
observe one thing producing ai^i'other ; that we can at 
most observe that one thing is followed by another, and 
perhaps find reason for believing that it will always 
have such a connection ; and that to say that A pro- 
duces B, is to raise a metaphysical question with which 
science and everyday thinking are not concerned. But 
if we give up this way of conceiving cause, what can we 



82 INDUCTION 

put in its place? Is it sufficient to say that cause means 
simply invariable succession? No, for the succession of 
day and night is an invariable succession. The notion 
of cause implies that the relation of cause and effect 
not only is invariable, but also that it must be so ; that 
there is an unconditional or necessary connection be- 
tween the two ; that if the first does not happen, the 
second cannot. In the field of physical phenomena, it 
is held also that the amount of energy in the cause is 
exactly equal to the amount of energy in the sum-total 
of its effects ; in other words, that no energy is either 
lost or created. This is known as the Law of the Con- 
servation of Energy. Whether it applies where mental 
phenomena are concerned has been questioned. How- 
ever this may be, cause always means unconditional 
connection.^ Two things stand in a relation of causal 
connection when they are so related that one is the un- 
conditional accompaniment of the other ; the cause usu- 
ally occurs or begins before the effect, but there are 
cases in which both seem to begin together. Heat is 
a cause of expansion, but a body does not first become 
hot and then expand; the two phenomena occur simul- 
taneously, A causal law is a statement, in general 
terms, of a causal connection. Thus : " Heat causes ex- 
pansion." 

The sort of generalization which is most frequently 
of interest and importance is one which asserts a con- 
nection of this sort, although this is not the only sort 
which may be investigated. For instance, the universal 



2 Of course, the fact that a connection is unconditional cannot 
be observed. The reasons for asserting that it is unconditional 
will appear presently. 



CO-EXISTENCE AND CAUSATION 83 

concurrence of two properties in a given substance may 
be a matter of importance, but their connection would 
not be called a causal connection. The specific gravity 
and the atomic weight of carbon would be a case in 
point. The co-existence of gravity and inertia is an- 
other example mentioned by Bain ; the sciences furnish 
mnumerable instances of a like sort. Bain remarks that 
" there are very few general laws of pure co-existence ; 
causation is singular in providing a comprehensive uni- 
formity that may be appealed to deductively for all 
cases. The uniformities of co-existence (independent 
of causation) can be proved only piecemeal; each stands 
on its own evidence of observation in detail ; no one 
assists us to prove another." The causal law is the one 
to which we shall give most attention. 

Testing Inductive Inferences. — We return to the 
question, " How can we prove an inductive inference to 
be true? How can we show that it is a law.? '' There 
are several things which would show that it was not 
true ; if we found that there were facts which were in- 
consistent with it, or if it were found to be inconsistent 
with itself, or if it proved to be in disagreement with 
any established law, it could be rejected at once. But 
suppose that none of these things were found ; should 
the inference be accepted as true.? Not necessarily; it 
might be that our observation or our reflection on the 
case had been insufficient to show us exceptions or in- 
consistencies if such did exist. If w^e have inferred a 
universal connection we are very likely to overlook 
exceptions or to forget those which we have observed. 
A good many people still believe that Friday is an un- 
lucky day and that the number 13 brings misfortune. 



84 INDUCTION 

But even If no exceptions have occurred and if the in- 
ference is not inconsistent with known laws, how can 
we he assured that exceptions may not occur in the 
future^ or that further reflection might not discover 
fatal inconsistencies? A large number of favorable 
cases is not alone sufficient to give this assurance. The 
example of the succession of day and night illustrates 
that. Millions of cases do not prove inevitable con- 
nection. On the other hand, a single experiment made 
by some scientist in his laboratory may be sufficient to 
establish some very important law. " Why/' asks Mill, 
-^ " is a single instance in some cases sufficient for a com- 
plete induction, while in others myriads of concurring 
instances, without a single exception known or pre- 
sumed, go such a very little way towards establishing 
an universal proposition? Whoever can answer this 
question knows more of the philosophy of logic than the 
wisest of the ancients, and has solved the problem of 
Induction." Mill himself aided very materially In the 
formulation of the conditions under which we do regard 
our inductive inference as established, and the inductive 
methods presently to be discussed are usually called 
" Mill's methods." Whether or not he has solved the 
whole problem of Induction is another question and one 
with which we shall not at present concern ourselves. 
V Complete Enumeration. — There are cases in which 
the establishment of universal conclusion might seem 
to be comparatively easy. It is sometimes possible that 
all the cases of a given sort may have been observed. 
For example, observation has shown that Mercury re- 
volves about the sun; that Venus does also; and like- 
wise of the Earth, Mars, Jupiter and each of the other 



COMPLETE ENUMERATION 85 

planets. We can say then with perfect safety, that all 
the planets ^ revolve about the sun. The universal 
statement is warranted because each of the instances 
which it covers has been observed. We are saying no 
more in the conclusion than we had already said in the 
several statements on which the conclusion is based. 
The universal is, in fact, simply a summary way of 
expressing what had already been said. It is merely a 
" telescoping " of the other statements, as it were. This 
act of basing a general statement on a complete enum- 
eration of the particular cases which it covers has been 
called Perfect Induction, It was so called because the 
conclusion is one which possesses complete certainty, 
whereas most inductive inferences are more or less un- 
certain. It might seem then that this was the solution 
of the problem raised above ; you are sure of your uni- 
versal if you have seen all the particulars which it 
covers. But how can we be sure that we have counted 
all the particulars? The field of observation may be 
so small and so easily explored that every existing case 
may be observed. But even if all existing cases have 
been observed, how can we be sure that others mav not 
arise, and that they may not differ from those we have 
observed? We may have such knowledge about a class 
of objects as will enable us to say that if any other 
members of the class should come into existence they 
would be like those already known. We may know 
that the sum of the angles of every plane triangle 
which may ever exist will be equal to two right angles, 
not because we have counted cases, but because we know 
that this necessarily follows from the properties essen- 
3 Leaving the asteroids out of consideration. 



86 INDUCTION 

tial to all triangles. However numerous the class 
which has been completely observed, the knowledge 
that each of the observed members stands in certain 
relations does not by itself assure us that other con- 
ceivable members of the class would be like them in this 
respect. Complete enumeration is useful as an abbre- 
viated way of stating certain kinds of information, but 
it throws no light on the methods of discovering uncon- 
ditional connections.^ 

The judgments which result from the complete enum- 
eration of cases have been called, by some writers, 
Enumerative Judgments and by others, Collective Judg- 
ments. 

How Generalizations can be Verified— It appears 
then that enumeration of all the existing members of 
a class does not enable us to establish laws. Anything 
short of that might seem to leave us still farther from 
that goal. And it is of course true, as appeared on 
page 84, that an incomplete enumeration of instances 
furnishes no verification. Then if verification is pos- 
sible at all it can not rest on mere enumeration, or 
counting of cases. Suppose that the observation of one 



4 It may be well to note one case in which a statement in 
the universal form must be distinguished from a law. As an 
example, we may take, " Every three-sided figure is a triangle/' 
This is not an inductive inference; it is not based upon the ob- 
servation of individual instances at all. It is true in all cases, 
but it is true because we have previously said, " If any figure 
has three sides we will call it a triangle." In other words, it is 
true hy definition. It is like an inductive generalization in apply- 
ing to all possible cases, past, present and to come, real and 
imaginary, etc., but it is not based upon the observation of in- 
dividual facts. Other judgments and operations, which must be 
distinguished from those which are present in induction properly 
so called, will be discussed in a later chapter: and still others 
may be found by referring to Mill's Logic, Book III, chapter ii. 



VERIFICATION 87 

or more instances in which B has followed A has sug- 
gested to us the inference that A and B are causally 
related. Let us ask ourselves what consequences would 
follow upon the truth of this inference. In the first 
place we could conclude that if B were present in any 
case A must have been present also; and, again, if A 
were absent in any case, its supposed effect B must have 
been absent also ; or if either A or B varied in amount 
or degree the other should show a corresponding varia- 
tion. All these things should be true of phenomena 
which are causally related. Phenomena which failed 
to satisfy such conditions could not be unconditionally 
connected. Suppose we had inferred that absence of 
oxygen would cause death. If that is true, an animal 
immersed in nitrogen should die. If experiment showed 
that an animal could live under such conditions, our 
inference would, of course, be disproved; but suppose 
the animal did die, would the inference be proved.^ Not 
necessarily. Perhaps the nitrogen acted as a poison 
or perhaps the death of the animal was due to rough 
handling, etc. Our inductive inference would be com- 
pletely verified only if we could show that death could 
not have been due to anything except the absence of 
oxygen. If we could be sure that all the circumstances 
wfiich were present before the experiment remained pre- 
cisely the same with the one exception that oxygen was 
present in the first case and absent in the second, then 
we should have shown a necessary connection between 
the absence of oxygen and the occurrence of death. 
Nothing else could have been the cause because all were 
present when death did not occur. If a second circum- 
stance were present when the phenomenon occurred and 



88 INDUCTION 

absent when it did not occur, it would dispute with the 
first the right to be called the cause and no final con- 
clusion would be possible. When all other possibilities 
can be excluded, the one which remains is the cause. 
When no other inference is consistent with the facts, 
the one which is consistent must be accepted as true. 
^w We can say, then, that an inductive inference is com- 
pletely/ verified when we have found facts which are con- 
sistent with its truth and inconsistent with any possible 
rival inference; or more briefly, when it fits the facts 
and no alternative inference does. We establish one in- 
ference by eliminating all others. We reason that the 
phenomenon under investigation has some cause ; this 
other phenomenon, A, may be the cause; it fulfills the 
requirements and no other does ; therefore, this one is 
and must be the cause in question. There are several 
ways of selecting or grouping instances so as to show 
that some one factor alone satisfies the requirements. 
These are known as the Inductive Methods. 

Observation, and Analysis are Presupposed. — One 
thing should not be forgotten. It is that the application 
of such principles as these presupposes very careful ob- 
servation ; if we are to be certain that no other circum- 
stance is present when a given phenomenon is present 
or absent when it is absent, we must have observed all 
the other circumstances. In ordinary observation we 
note only a few of the circumstances ; if we are un- 
trained observers it may be impossible for us to ob- 
serve more than a few. It is quite impossible for a child 
to observe in a flower all that a trained botanist can 
observe there. Accurate observation presupposes anal- ■ 
ysis, i. ^., breaking up the total complex phenome- 



TEST CONDITIONS 89 

lion into its element. The beginner in any science Is 
unable to handle the facts properly because he Is un- 
able to analyse them ; he sees only their most obvious 
characteristics. 

Postponing Inference till Test Conditions are Pres- 
ent — Before we begin the more detailed examination of 
the methods of verifying an Inductive inference, there 
is one more statement to be made, namely this : Instead 
of making a generalization and then searching for 
means of verifying it, we may refrain from drawing 
any inference until we have before us a group of facts 
which will make it possible to draw a correct inference. 
In other words, we may make our inference under test 
conditions. Suppose, for example, that we are trying 
to discover the cause of eclipses. Before making any 
theories on the subject we might observe a number of 
cases. If we found that whenever an eclipse occurred 
there was an opaque body between us and the source 
of light and that at other times everything was the 
same except that there was no body in that position, we 
should infer at once that the presence of the opaque 
body in that position was the cause of the eclipse. And 
so in any other case we might form no theory until we 
had facts which would make it possible to form a cor- 
rect one. 

" If a chemist discovers a new element, he will pro- 
ceed to try a variety of experiments In order to de- 
termine the proportions In which It will combine with 
other elements as well as to discover the various prop- 
erties of such combinations. Supposing such experi- 
ments to have been properly conducted, the Inductions 
at which he arrives will be perfectly valid, though he 



90 INDUCTION 

may have formed no previous theories as to the results 
of his researches. Occasionally, too, an induction will 
not be the result of any definite course of investigation, 
but will be obtruded on our notice." ^ But such cases are 
rare, and ordinarily we have some theory before we have 
the facts which will verify it. 

It is often better to draw an inference early in the 
investigation ; the reasons for this will be discussed in 
a later chapter.^ In the meantime it should be remem- 
bered that the Inductive Methods which are now to be 
discussed may be used either to test an inference al- 
ready made or to furnish a basis for drawing a correct 
inference if none has previously been drawn. 
V The Inductive Methods. — I. Agreement. Sup- 
pose we find that A was followed by B in a number of 
instances, but that the attendant circumstances varied 
greatly. Suppose, for example, that three or four in- 
dividuals, of different races, different habits of life, 
and otherwise as different as possible, were all bitten 
by a certain kind of mosquito and that each developed 
yellow fever: would not such a set of cases give some 
warrant to the inference that the bite of the mosquito 
was causally connected with the development of the 
fever? The fact that these individuals were different 
in all other respects would seem to exclude the possi- 
bility that anything else could have been the cause. 

Or suppose again that we find dew deposited on two 
or more objects which differ in position, chemical com- 
position, character of surface, and, in short, all respects 
except that both are cooler than the surrounding atmo- 

5 Fowler, Inductive Logic, p. 11. 

6 Part III, chapter ii, Hypothesis, 



THE METHOD OF AGREEMENT 91 

sphere; we should have good grounds for believing that 
this last characteristic was causally related to the dep- 
osition of dew. 

Or, once more, if a number of persons who recovered 
from a given disease were similar only in having used 
a certain drug, the inference would be that the drug 
was causally related to the cure. 

In each of these examples we have a set of instances 
in which a given phenomenon is present, an attack of 
fever, deposition of dew, recovery from illness; nothing 
else is present in all cases except one other phenomenon, 
being bitten by the mosquito, being cooler than the 
surrounding air, having used a certain drug. Our infer- 
ence is that the phenomena which are constantly pres- 
ent together are causally related. If A is causally, i. e., 
unconditionally, related to something else, that thing 
must be present when A is present. As only one other 
phenomenon is present in all cases, that alone among 
all those at any time present can be causally related 
to the first. This method of isolating the phenomena 
which are so related is known as the Method of Agree- 
ment. Mill's statement of the Canon of Agreement is 
as follows : " If two or more instances of the phenom- J'^ 
enon under investigation" [fever, deposition of dew, 
etc.], " have only one circumstance in common " [being 
bitten by a mosquito, being cooler than the surrounding 
air, etc.], " the circumstances in which alone all the in- 
stances agree is the cause (or effect) of the given phe- 
nomenon." His statement of the axiom of this method 
is: " Whatever circumstance can he excluded without 
prejudice to the phenomenon^ or can be absent notwith- 
standing its presence, is not cormected with it in the way 



92 INDUCTION 

of causation.''^ The only circumstance which is com- 
mon to a number of instances in which a given phe- 
nomenon is present, is causally related to it, because all 
the rest are excluded by the fact that they are separable 
from it. 

In this method, as in the others to be discussed, 
the point of first importance is that we are selecting 
instances of the occurrence of a phenomenon, and 
selecting them in such a way as to identify the cir- 
cumstance or circumstances causally related to the 
phenomenon. We might re-word the main points as 
follows: select instances in which the phenomenon under 
investigation is present, but which are as different as 
possible in all other respects ; if there is one circum- 
stance and one only which is always present when the 
phenomenon under investigation is present, that cir- 
cumstance is causally related to the phenomenon. 

Difficulties in Using this Method. — An ideal case 
might be represented symbolically in this way : let the 
phenomenon under investigation be represented by a^; 
and let the accompanying circumstances, in the several 
instances we have selected be represented by abcde, 
afghi, ajMm, respectively ; or the phenomenon and its 
accompanying circumstances by : 

ahcdex 
afghix 
ajklmx. 

The only circumstances common to all the instances is 
a. Therefore a is causally related to x. No actual 



DIFFICULTIES 93 

case would be quite so simple ; any phenomenon has 
among its accompanying circumstances everything that 
is happening in the universe at the time of its occur- 
rence. Most of these circumstances can, of course, be 
eliminated as irrelevant ; still it is easily possible to 
overlook something that is relevant. 

1. Circumstances which might seem to have no con- 
nection with the phenomenon may be causally related 
to it. For example, it might be supposed that the 
number of sun-spots had no relation to financial con- 
ditions ; yet it has been shown that the periods when 
sun-spots are most numerous have the same frequency 
as the periods when panics occur ; and it has been sug- 
gested that sun-spots influence climatic conditions, that 
these in turn, by influencing crops, and so on, do aff'ect 
financial conditions. Whether there is any truth in this 
or not, it will remind us that it is not easy to determine 
just what circumstances are relevant. 

2. Another difficulty arises from the fact that analj^- 
sis is never complete ; not all the elements are singled 
out, and some of those which have been overlooked may 
be all-important. For example : it had been noticed that 
persons who had been much out of doors at night were 
more likely than others to be attacked by malaria; it 
was inferred that " night-air " was a cause of malaria, 
and consequently people tried to exclude it from their 
houses. Later it was shown that the attacks of mos- 
quitoes were the causes. Mosquitoes are more active at 
night, but instead of noting this, the more obvious fact 
that " night-air " is damp, and so on, was selected as 
the important one. When it was found that the bite 



94 INDUCTION 

of the mosquito was the circumstance always present, 
while the time of the attack made no difference, the 
older theory was overthrown. 

In symbolizing an actual case we should need some- 
thing to represent the circumstances which were dis- 
regarded or overlooked. We might use the symbol 
X; the accompanying circumstances would then be rep- 
resented by ahcde. ,X^ afghi. .X, etc. This would in- 
dicate that there is a margin of uncertainty in such 
cases. 

S. There is one other difficulty in the application of 
the method of Agreement. It may be illustrated in this 
way : suppose a man should drink coffee with his lunch- 
eon on one day and afterwards smoke a strong cigar; 
suppose on the following day, with a different bill of 
fare, he should drink tea and smoke a cigar; on both 
days he has a headache in the afternoon. The applica- 
tion of the method of Agreement would lead him to be- 
lieve that the cigar was the cause of the headache, 
whereas the cause may have been the coffee in one in- 
stance and the tea in the other. This illustrates what 
is known as the Plurality of Causes, A given phenome- 
non may have one cause in one instance and another 
cause in a second instance. It is sometimes said that if 
our analysis were complete we should find that a given 
phenomenon always had the same cause ; that in the in- 
stances iust mentioned, the cause of the headache wa3 
something common to tea and coffee ; or that the head- 
ache caused by coffee differs from that caused by tea 
and that two things which are different never can pro- 
duce the same effect. Perhaps that is true, but the fact 
still remains that, in practice, effects which are so simi- 



THE METHOD OF DIFFERENCE 95 

lar as to be indistinguishable may be produced by causes 
that, for ordinary observation, are very different. This 
makes a very serious Hmitation to the appHcation of 
the method of Agreement. The method is still valuable 
as suggesting causal relations, though imperfect as a 
means of proof. May it not be possible to select in- 
stances on some other principle in such a way as to 
obviate some of these difficulties .^^ 

II. The Method of Difference. — Take another 
concrete case: suppose two individuals as similar as 
possible in all respects, race, family, occupation, man«r 
ner of living, state of health and so on ; one of these 
is bitten by mosquitos of a certain sort and the other 
protects himself against their attacks ; the first con- 
tracts the fever, the second escapes it. We should 
regard such a group of facts as warranting the conclu- 
sion that the bite of the mosquito and the contraction 
of yellow fever were causally related. 

Or, if two objects of similar chemical construction, 
character of surface, location, etc., differed only in that 
one was for some reason cooler than the surrounding 
air, while the other was not, and if dew were deposited 
on the first and not on the second, we should conclude 
that the cooler temperature of the one was causally 
related to the deposition of dew upon it. 

Cases like these illustrate the Method of Difference. 
Mill's statment of the Canon of this method is : 

" If an instance in which the phenomenon under in- 
vestigation occurs, and an instance in which it does not 
occur, have every circumstance in common save one, 
that one occurring only in the former; the circum- 
stance in which alone the two instances differ is the 



96 INDUCTION 

effect or the cause, or an indispensable part of the 
cause, of the phenomenon." Its axioms, in the words 
of the same writer, are: " Whatever antecedent can be 
excluded without preventing the phenomenon, is the 
cause, or a condition of the phenomenon; whatever con- 
sequent can he excluded with no other difference in the 
antecedents than the exclusion of a particular one, is 
the effect of that one,^^ 

Relation of this to the First Method.— ^^ quote 
from Mill again regarding the relation of this method 
to the other: 

" Instead of comparing different instances of a phe- 
nomenon to discover in what they agree, this method 
compares an instance of its occurrence with an instance 
of its non-occurrence, to discover in what they differ. 
. . . Both are methods of elimination, . . . The 
Method of Agreement stands on the ground that what- 
ever can he eliminated is not connected with the phe- 
nomenon hy any law. The Method of Difference has 
for its foundation, that whatever cannot he eliminated 
is connected with the phenomenon hy a law.^^ 

Incomplete analysis of the circumstances attending 
the phenomenon may vitiate the inference in both 
methods : in the method of Agreement as already 
stated; in the method of Difference, by leading us to 
overlook points of difference in cases supposed to be 
alike except in the particulars specified in the Canon 
of this method. 

Difficulties in Using the Method of Difference.— 1. 
One^ danger in employing the method of Difference 
results from the possibility of the Composition of 
Causes. It often happens that a given phenomenon 



DIFFICULTIES 97 

IS the effect of the joint action of several causes. Heat, 
light, moisture, etc., are all causally related to the life 
of plants. If two plants were similarly situated as 
regards all but moisture, it would be incorrect to con- 
clude that moisture was the sole cause of the life of 
the one because its absence was followed by the death 
of the other. Application of the method of Difference 
does show that the antecedent is causally related to the 
consequent, but not that it is the sole or adequate cause. 

If we could supplement the method of Difference by 
the method of Agreement, if we could find a set of in- 
stances in which the supposed cause was alone common 
to the cases in which the phenomenon was present, then 
we could conclude that this supposed cause was ade- 
quate to produce the phenomenon. 

2. Another source of difficulty closely connected with 
the one just discussed is to be found in the existence of 
Counteracting Causes, Even if a cause is adequate to 
the production of an effect under ordinary conditions, 
it may fail to produce it owing to the presence of some 
opposed tendency. The poison can be counteracted by 
an antidote ; the tendency of the moon to fall to the 
earth is in part overcome by centrifugal force, and so 
on. The presence of a counteracting cause might lead 
us to overlook the real cause of the phenomenon. The 
cause is present without the effect ; that is, without the 
usual effect. In such a case its effect is to be found in 
its modification of the counteracting cause. The ten- 
dency of the moon to fall does modify the effect which 
would otherwise be produced by its tendency to fly off at 
a tangent. We may symbolize one sort of case in which 
error might arise, as follows : Let m be the phenomenon 



98 INDUCTION 

whose cause we are seeking and suppose that we have 

abed X 
abcr X m 

We should probably conclude that r was the cause of 
m, whereas it might well be that a was the real cause, but 
that it was counteracted in the first instance by d. It 
is no doubt true that in an ideal application of the 
methods there would be little difficulty ; if we could get 
cases which differed in only one circumstance it would 
at any rate be easy to see that the absence of the effect 
m was connected with the presence of the circumstance 
d; we should still have to search for the cause of ins 
presence. But in actual cases the matter is not so sim- 
ple; we cannot find ideal cases and the instances we 
select for the application of the method of Difference 
may differ in more than one respect, as in the case just 
discussed. 

III. The Joint Method. — Nature presents very 
few instances in which the method of Difference can be 
directly applied, and even experiment fails to present 
ideal conditions. It seldom happens that the conditions 
stated in the Canon of Difference are realized. The 
same is true to a great extent with regard to the method 
of Agreement. Usually two or more cases in which a 
given phenomenon occurs are similar in more than one 
circumstance. In such cases it is sometimes possible to 
use a combination of the two methods. The following 
instance illustrates the use of The Joint Method of 
Agreement and Difference: a, large number of cases of 
typhoid fever occurred at about the same time in a 
college community. It hapjDened that all those who de- 



THE JOINT METHOD 99 

veloped the disease ate at a certain few fraternity and 
boarding-house tables. The water supply was first in- 
vestigated. It was found that all these places used 
water from the same source. But it was also true that 
the other houses were supplied from the sgtme source, 
so this possible cause was eliminated. The fresh vege- 
tables were supplied from various sources ; some of the 
places in which the disease was developed used one 
source, others a different one ; moreover, the places in 
which the disease was not developed were supplied from 
the same variety of sources. The other food supplies 
came from various places and the method of Agreement 
could not be applied so far as they were concerned, with 
one exception ; it appeared that the milk supply was the 
same for all the places in which the fever was developed, 
whereas none of the places which escaped used milk 
from that source. The inference was that the milk 
contained the cause of the disease. Further, it was 
found that when milk from this source was no longer 
used, no new cases of the disease appeared. There were 
two sets of cases : in one the disease was developed, in 
the other it was not. Those in which it appeared were 
alike in several respects ; the ages, habits and previous 
general health were similar in all ; the water supply was 
the same and also the milk supply ; it might be any one 
of these ; the method of Agreement could not be suc- 
cessfully applied. The other set of cases, those in which 
the disease did not appear, were like the first in many 
respects, but there was no one of these which differed 
from any one of the others, in one respect only. There 
was one and one only circumstance in which all the 
members of the first group differed from all the mem- 



100 INDUCTION 

bers of the second, namely In the milk supply. All of 
one group agreed in having a given milk supply and 
developing typhoid fever; all of the other group 
agreed in using milk from another source and escaping 
the disease. Comparing group with group the method 
of Difference could be used. There was only one cir- 
cumstance in which all the instances in which fever was 
developed differed from all of those in which it was not 
developed. Within each set of instances there is a 
partial application of the method of Agreement. One 
set agreed in having the disease and also in having an- 
other common circumstance ; but more than one circum- 
stance was common, so the application could not be 
complete; similarly the other set of instances agreed 
in the absence of the fever and in the absence of this 
circumstance ; but they also agreed in lacking va- 
rious other circumstances. However, they agreed 
in lacking only one which was present in all those 
of the other set, and that is the important 
point. 

The two sets of instances might be symbolized thus ; 
p representing the phenomenon under investigation: 

ahcdr X p bckr 

abefr X p eflr 

aefgr X p fgmr 

afghrX p ghnr 

Both a and r are common to all the instances in which p 
is present, but r is excluded by the fact that it is pres- 
ent in those in which p is absent. 

Mill's statement of the Canon of the Joint Method 
reads : " If two or more instances in which the phe- 



THE JOINT METHOD 101 

iiomenon occurs have only one circumstance in com- 
mon, while two or more instances in which it does not 
occur have nothing in common save the absence of that 
circumstance, the circumstance in which alone the two 
sets of instances differ is the effect or the cause, or an 
indispensable part of the cause, of the phenomenon." 
This statement does not quite cover a case like that 
described above. The instances in which the phenome- 
non occurs may have more than one circumstance in 
common, provided that there is only one which is at the 
same time common to these and absent from those in 
which the phenomenon does not occur. We might re- 
state it thus : " If two or more instances in which a 
phenomenon occurs have in common one ^ circumstance 
which is at the same time the only circumstance present 
in these instances and absent from two or more instances 
in which the phenomenon does not occur, that circum- 
^ stance is causall}^ related to the phenomenon.'' This 
form of statement avoids the difficulty just mentioned 
and also another. It is practically impossible to find 
a set of instances w^hich have nothing in common save 
the absence of one circumstance. In the example just 
given, the instances in which typhoid fever did not oc- 
cur agreed in not being Esquimaux nor octogenarians 
nor coal-miners, and so on indefinitely. On the other 
hand it would have been easily possible to find a group 
of instances in which there would have been fewer cir- 
cumstances absent from all. One might select a num- 
ber of individuals from different races, of different ages, 
occupations, and so on. Fewer circumstances would be 
absent from all of these than from a homogeneous group 
of college students. But such instances might be en- 



102 INDUCTION 

tirely insignificant for the purpose of discovering the 
cause of the disease. Of course, if the group of nega- 
tive instances included examples from all varieties of 
those who lacked the phenomenon in question, and we 
could discover the only circumstance lacking in these, 
and present in the cases where the phenomenon w^as 
present, a conclusion could be drawn ; but, in the first 
place, it would be impossible to get such a group, for 
it would be infinite in extent ; and, secondly, if the group 
could be had, the discovery of the onl}^ circumstance 
lacking from all of them would be an endless task. Most 
of such instances might at once be eliminated as irrele- 
vant, though Mill's canon does not provide for that. 
It is important that the instances in which the phe- 
nomenon is absent should be similar to those in which 
it is present, for if there are many points of difference 
it will be difficult or impossible to select those which are 
causally related to the phenomenon. 

IV. Concomitant Vauiations. — There are still 
other methods of discovering causal relations. Suppose 
a case in which such instances as are demanded for the 
application of any of the foregoing methods cannot be 
obtained; it may be possible to find instances in which 
the phenomenon occurs in varying degrees or in dif- 
ferent quantities, while some other phenomenon varies 
concomitantly. " The effects of heat are known only 
through proportionate variation. We can not deprive 
a body of all its heat ; the nature of the agency forbids 
us. But by making changes in the amount, we ascer- 
tain concomitant changes in the accompanying cir- 
cumstances, and can so establish cause and effect. It is 
thus that we arrive at the law of the expansion of bodies 
by heat. In the same way we prove the equivalence of 



1 



CONCOMITANT VARIATIONS 103 

heat and mechanical force as a branch of the great 
law of Conservation of Persistence of Force." 

" The proof of the First Law of INIotion, as given 
by Newton, assumed the form of Concomitant Varia- 
tions. On the earth, there is no instance of motion 
persisting indefinitely. In proportion, however, as the 
known obstructions to motion — friction and the resist- 
ance of the air — are abated, the motion of a body is 
prolonged. A wheel spinning in an exhausted receiver 
upon a smooth axle runs a very long time. In Borda's 
experiment with the pendulum, the swing was prolonged 
to more than thirty hours, by diminishing the friction 
and exhausting the air. Now, comparing the whole 
series of cases, from speedy exhaustion of movement to 
prolonged continuance, we find that there is a strict 
concomitance between the degree of obstruction and the 
arrest ; we hence infer that if the obstruction were en- 
tirely absent, motion would be perpetual. The statis- 
tics of crime reveal causes by the method of Variations. 
When w^e find crimes diminishing according as labor is 
abundant, according as habits of sobriety have in- 
creased, according to the multiplication of the means of 
detection, or according to the system of punishments, 
we may presume a causal connection, in circumstances 
not admitting of the method of Difference." '^ 

We may symbolize a set of instances to which this 
method is applicable in this way : 

a bed X p 
\{^a) bee X (2p) 
(4a) bef X (3p), etc. 

The Canon of the Method of Concomitant Variations 

7 Bain, Logic, pp. 62-63. 



104^ INDUCTION 

is : " Whatever phenomenon varies in any manner 
whenever another phenomenon varies in some particular 
manner, is either a cause or an effect of that phenome- 
non, or is connected with it through some fact of cau- 
sation. '^ 

V. The Method of Residues. This method is 
usually included with the others and completes the list. 
Its canon is : " Subduct from any phenomenon such 
part as is known by previous inductions to be the effect 
of certain antecedents, and the residue of the phenom- 
enon is the effect of the remaining antecedents." Its 
principle, like that of the other methods, is that of ex- 
clusion. If we have a complex phenomenon or a group 
of phenomena represented by the letters xyzlm, and a 
group of antecedent circumstances represented by 
abcdf^ and if we know that a causes x and b causes «/, c 
causes z and d causes Z, the conclusion will be that the 
remaining m is the effect of f. This method would be 
equally applicable in an instance in which the causes 
were present with the effects instead of being ante- 
cedent to them only. Thus, if we had a phenomenon 
m in a group of circumstances, abcdfxyzlm, and knew 
as before that a and ^, b and y, c and z, and d and I 
were causally related, the connection of / and m would 
be evident. We must, of course, be careful to include 
all the relevant circumstances in the group. 

If a phenomenon has occurred and all the know^n ante- 
cedents of this phenomenon are known not to contain 
its cause, the cause must be sought for in some phe- 
nomenon not yet discovered. There were certain per- 
turbations in the movement of the planet Uranus, not 
accounted for by the attractive force of any known 



THE METHOD OF RESIDUES 105 

heavenly body ; they must, then, be due to some body 
not yet discovered ; this line of reasoning led to the dis- 
covery of the planet Neptune. 

Again, the weight of atmospheric nitrogen was 
found to be greater than that of nitrogen produced 
chemically; further examination revealed the presence 
in the atmosphere of another element, argon. 

Obviously the method of Residues can be applied 
only when we have fairly complete knowledge of the 
field of facts in which the phenomenon is found. We 
must know the causal relations of all the circumstances 
involved in the case except the phenomenon under inves- 
tigation. 

The following example, though not formally in- 
cluded under Mill's canon, employs the principle of 
Residues : If only four men were capable of doing a cer- 
tain act and if we learned that one of these was tempo- 
rarily unable to do it, through illness, and that the two 
others were a thousand miles away when the act was 
performed, the fourth must have committed the act. 
If, in any may^ we can assure ourselves that of all the 
possible causes of a phenomenon all but one are ex- 
cluded, that one must be the cause. The several methods 
are ways of doing this. 

EXERCISES 

Examine the following arguments and criticise the rea- 
soiring as fully as possible; state the method used: 

1. The newly discovered painting must be a Rubens; 
for the conception^ the drawing, the tone and the tints are 
precisely those seen in the authentic works of that master. 
(Hyslop.) 



106 INDUCTION 

2. In nine counties^ in wliicli the population is from 100 
to 150 per square mile, the births to 100 marriages arc 396; 
in sixteen counties, with a population of 150 to 200 per 
square mile^ the births are 390 to 100 marriages. Therie- 
fore the number of births per marriage is inversely related 
to the dens^ity of population and contradicts ]\Ia]tluis's 
theory of the law of po[)ulation. (H^^slop.) 

3. The great famine in Ireland began in 1845 and in- 
creased until it reached a climax in 1818. During this 
time agrarian crime increased very rapidly until, in 1848^ 
it was more than tliree times as great as in 1845. After 
this it decreased with the return of better crops until^ in 
1851^ it was only 50 per cent, more than in 1845. It is 
evident from this tliat a close relation of cause and elFect 
exists between famine and agrarian crime. (Hyslo}).) 

4. The influence of heat in changing the level of the 
ground upon whicli the temple of J u}) iter Serapis stands 
might be inferred from several circumstances. In the first 
place^ tliere are numerous hot s})rings in the vicinity^ and 
when we reflect on the dates of the principal oscillations of 
level this conclusion is made much more })robable. Thus, 
before the Christian era, when Vesuvius was regarded as a 
spent volcano, the ground on which the temple stood was 
several feet above water. But after the eru})tion of Vesu- 
vius in 79 B. c, the temple was sinking. Subsequently 
Vesuvius became dormant and the foundations of the tem- 
ple began to rise. Again Vesuvius became active, and has 
remained so ever since. During this time the temple has 
been subsiding again, so far as we know its history. 
(Hyslop.) 

5. Take a bottle of charged water, slightly warmer than 
a given temperature registered by the thermopile, and mark 
the deflection it causes. Then cut the string wliicli holds it 
and the cork will be driven out by the elastic force of the 
carbonic acid gas. The gas performs its work, and in so 
doing it consumes heat and the deflection of the thermopile 
shows that the bottle is cooler than before, heat having 

^been lost in the process. (Hyslop.) 

6. As an evidence of the extreme antiquity of highly 
civilized man, we have the following facts : On one of the 
remote islands of the Pacific — Easter Island — two thousand 



EXERCISES 107 

miles . from South America^ two thousand miles from the 
Marquesas^ and more than one tliousand miles from the 
Gambier Islands^ are found hundreds of gigantic stone 
images^ now mostly in ruins. They are often forty feet 
high^ while many seem to have been larger, the crowns of 
their heads, cut out of red stone, being sometimes ten feet 
in diameter, while even the head and neck of one is said 
to have been twenty feet high. The island- containing 
these remarkable works has an area of about thirty square 
miles, and as the smallest image is about eight feet high, 
weighing four tons, and as the largest must weigh over a 
hundred tons or much more, their existence implies a large 
population, abundance of food, and an established govern- 
ment which so small an island could not supply. (Flyslop.) 

7. We observe very frequently that very poor handwrit- 
ing characterizes the manuscripts of able men, while the cc^i. 
best handwriting is as frequent with those who do little "/ 
mental work when compared with those whose penmanship 'M/^ 
is poor. We may, therefore, infer that poor penmanship 

is caused by the influence of severe mental occupation. 
(Hyslop.) 

8. In the following instances crystallization takes place: 
the freezing of water; cooling and solidifying of molten 
metals and minerals; deposition of salts from solutions; 
volatilization of solutions ; deposition of solids from the 
gaseous state, as iodine; pressure; slow internal change, as 
in rocks ; the transformation of metals from the tough to 
the brittle condition, by hammering; vibration, and re- 
peated heatings and coolings. We may then conclude that 
the cause of crystallization is the increased scope and oper- 
ation of the molecular or solid-forming cohesion. (Bain.) 

9. When the barometer was carried to the top of the Puy 
de Dome it was found that the mercury stood lower than 
before. It was inferred that the pressure of the air was 
the cause of the rise of mercury in the tube. 

10. The chemical action between two substances is much 
greater when they are in a liquid than when they are in a 
gaseous state. We may conclude that there is an inverse 
relation between cohesion and chemical activity. 

11. Goldscheider proved that muscular sensations play 
no considerable part in our consciousness of the movement 



:^irvu<:>«^ 



108 INDUCTION 

of our limbs_, by having his arm suspended in a frame and 
moved by an, attendant. Under these circumstances^ where 
no work devolved on the muscles^ he found that he could 
distinguish as small an angular movement of the arm as 
when he moved and supported it himself. 

He also proved that the chief source of movement-con- 
sciousness is pressure-sensations from the inner surface of 
the joints/ by having his arm held so that the joint sur- 
""^Hl^^ • faces are pressed more closely together^ and finding that 
a smaller movement was now perceptible. (Creighton.) 

12. '* That the Tempest belongs to the latest period of 
Shakespeare's literary activity is shown^ inter alia, by the 
absence of rhyme^ the large number of ' run on ' (un- 
stopped) lines^ the high proportion of weak and light end- 
ings^ and the comparative rarity of puns in the low scenes.'* 
(Mellone.) 

13. That the feeling of effort is largely^ if not entirely^ 
of peripheral origin^ appears from such experiments as the 
following: Hold the finger as if to pull the trigger of a 
pistol. Think vigorously of bending the finger^ but do not 
bend it. An unmistakable feeling of effort results. Re- 
peat the experiment, and notice that the breath is involun- 
tarily held, and that there are tensions in the other mus- 
cles. Repeat the experiment again, taking care to keep 
the breathing regular and the other muscles passive. Little 
or no feeling of effort will now accompany the imaginary 
bending of the finger. (Ferrier_, quoted by Hibben.) 

14. Sir Charles Lyell, by studying the fact that the river 
Ganges yearly conveys to the ocean as much earth as would 
form sixty of the great pyramids of Egypt, was enabled 
to infer that the ordinary slow causes now in operation 
upon the earth would account for the immense geological 
changes that have occurred, without having recourse to the 
less reasonable theory of sudden catastrophes. (Hibben.) 

15. Count Rumford in 1798 proved that the common 
notion that heat was a substance was false, by boring a 
large piece of brass, under great pressure of the bore, 
whilst the brass was in a gallon of water; and at the end 
of two and one-half hours the water actually boiled. (Hib- 
ben.) 

16. How would you set out to discover the causal rela- 



EXERCISES 109 

tions of the following phenomeira? Suggest instances and 
indicate the method to be used: 

(1) Heat and expansion. "-4^ ^ c^^y^ . 

(2) Heat and friction. ^^ «-<-«-. --^ , 

(3) Mosquitos and malaria. 

(4) The tubercle bacillus and consumption. 

(5) Golden-rod and hay fever. 

(6) A rainy spring and mosquitos. 

(7) The presence of oxygen and the burning of a 

candle flame. 

(8) Cocaine and the absence of pain. viA^ / 

(9) Moisture and vegetation. " ^ ' 

(10) The gulf -stream and climate. 

(11) The cause of the tides. 

(12) The cause of the trade winds. 

(13) The course of a glancing bullet. 

17. Cite ten cases of the composition of causes. 

18. Cite ten of the plurality of causes. 

19. Cite ten cases of counteracting causes. 

20. Bring in five cases illustrating each of the methods. 



CHAPTER VII 
VERIFICATION AND DEDUCTION 

Verification and Deduction. — All these methods 
are means by which a sound inference may be drawn or 
an inference already drawn may be verified. They all 
involve finding certain facts which inevitably follow 
from the inference in ques.tiotn, and they are not con- 
clusive if these facts can be shown to be consistent with 
any rival hypothesis. 

There is another way of testing the truth of any in- 
ference ; if we can show that the inference follows from 
something already known we shall establish the truth 
of the inference itself. Instead of searching for the 
consequences of the inferences and trying to determine 
their truth, we find a law of which our inference is it- 
self a necessary consequence. Conversely if an infer- 
ence is inconsistent with a known law it is necessarily 
false. In applying this it is necessary to remember 
that many supposed laws have proved to be false and 
that when an inference disagrees with a supposed law, 
it may be that the latter— or both — must be rejected. 
The fact that an inference is consistent with known 
laws does not prove its truth, but only its possible 
truth, for two rival hypotheses may be consistent with 
all the known facts and laws to which they are related. 
For proof, the connection must be closer than mere con- 
sistency. The inference must not only agree with the 
law, it must follow from it ; in other words, the truth 
of the law must insure the truth of the inference. 

110 



SYSTEMATIC KNOWLEDGE 111 

An inference from a law or general principle to some 
consequence of the principle is a deductive inference. 
When we reason in this way we reason deductively^ we 
deduce a conclusion, we employ deduction. 

Systematic Knowledge. — ^When we show that an in- 
ductive inference is a reliable statement of the relation 
of certain phenomena to each other, or when we show 
that any inference whatever is a consequence of some 
general principle, we establish the fact that the infer- 
ence with which we are dealing belongs to a system of 
facts or truths,^ In a system all the parts and elements 
are so related that the truth of one part implies the 
truth of the rest; we cannot hold to one part and reject 
the rest without inconsistency and contradiction. A sys- 
tem may consist of comparatively few members and be 
comparatively simple, as in an isolated syllogism, or it 
may be very broad in its scope and its internal relations 
may be exceedingly complex. For example, a philo- 
sophical system attempts to state the laws which hold 
for all reality. 

We shall begin our examination of systems with the 
syllogism. When we argue, to use the most ancient of 
illustrations, that " Socrates is mortal because all men 
are mortal and Socrates is a man," we are basing the 
truth of our conclusion upon a universal proposition, 
" All men are mortal," and the further proposition, 
" Socrates belongs to the class men." 

Criticism of the Syllogism. — It might be urged, as 
an objection to the syllogism, that "it gives us no new 

1 Professor Hibben in his Logic, Deductive and Inductive, 
makes much use of this conception in discussing the nature of 
deduction and induction. 



112 VERIFICATION AND DEDUCTION 

information ; if the conclusion is really contained in 
the major premise,^ as it must be if the reasoning is to 
be valid, why go to the trouble of making a syllogism? 
We knew beforehand that all members of the class 
designated by the subject were included in that desig- 
nated by the predicate, or possessed the quality, rela- 
tion, or whatever it may be, for which the predicate 
stands ; if we did not know that Socrates was mortal, 
how could we say that all men are mortal? Therefore, 
it is a matter of course that the subject of the conclu- 
sion, which is included in the subject of the major 
premise, will have that predicate. This objection would 
lead to the condemnation of such a science as geom- 
etry, for all its conclusions are contained in its postu- 
lates and axioms. Still we do get information by 
means of such processes. 

We may know it to be a g'oneral law that all iron 
compounds have certain properties without" knowing 
the chemical composition of a compound we have in our 
hands ; as soon as we discover that it is a compound of 
iron, we can draw our conclusion. Of course, if our 
major premise were not a law, our conclusion would 
not be trustworthy. If the general statement about 
iron compounds were an unverified inductive inference, 
then we could not state it with certainty so long as 
we were not sure that the present compound, if it proves 
to be iron, would possess the given properties. If all 
inductive inferences were simply enumerative or collec- 
tive judgments (page 86), if "perfect induction" 
were the ideal form of induction, then there would be 
ground for the objection we have mentioned. But if 

2 The universal proposition on which the reasoning is based, in 
this case, " All men are mortal," is called the major premise. 



VALUE OF THE SYLLOGISM US 

we may know that whenever a given phenomenon oc- 
curs, a certain circumstance must inevitably be pres- 
ent, or that any two properties are invariably con- 
nected, we have information which will apply to many 
cases of whose character we may yet be in ignorance. 
The syllogism is the typical fo-rm of reasoning. The 
quotation which follows is from Professor James's Psy- 
chology; it states the claim that reasoning is precisely 
that form of mental activity which does enable us to 
deal with new situations, with novel data. 

" A thing inferred by reasoning need neither have 
been an habitual associate of the datum from which we 
infer it, nor need it be similar to it. It may be a thing 
entirely unknown to our previous experience, something 
which no simple association of concretes could ever have 
evoked. The great difference, in fact, between that 
simple kind of rational thinking which consists in the 
concrete objects of past experience merely suggesting 
each other and reasoning distinctly so-called is this: 
that whilst empirical thinking is only reproductive, 
reasoning is productive. An empirical, or ' rule-of- 
thumb,' thinker can deduce nothing from data with 
whose behaviour and associates in the concrete he is un- 
familiar. But put a reasoner amongst a set of con- 
crete objects, which he has neither seen nor heard of 
before, and with a little time, if he is a good reasoner, 
he will make such inferences from them as will quite 
atone for all his ignorance. Reasoning helps us out 
of unprecedented situations — situations for which all 
our common associative wisdom, all the ' education ' 
which we share in common with the beasts, leaves us 
without resource.'' Psychology, Briefer Course, page 
352. 



114 VERIFICATION AND DEDUCTION 

As soon as we see that the present case belongs to a 
certain class or is of a certain type, the laws which are 
known to apply to that class or type may immediately 
be applied to it. 

How Propositions are Related to each other 

The syllogism as illustrated above shows that a univer- 
sal judgment may be made the basis for certain other 
statements. There are several kinds of syllogisms, but 
before discussing these it will be well to examine propo- 
sitions generally with a view to discovering what rela- 
tions different kinds of statements bear to each other 
and whether there may not be other ways than that 
illustrated in the syllogism, in which one statement may 
be made the basis for another. We have already dis- 
cussed four kinds of propositions ; those which are 
universal and affirmative, universal and negative, par- 
ticular and affirmative, and particular and negative. It 
will be remembered that the symbols for these were A, 
E, I, and O respectively. Their relations to each other 
are best shown by means of what is known as the 
" Square of Opposition," a diagram which has remained 
practically unchanged since the time of Aristotle. 

(All X is y) (No x is y) 

A Contraries E 



rO 



"^ I— H 

I Subcontraries O 

(Some x is y) (Some x is not y) 



RELATIONS OF OPPOSITION 115 

Let us take as an illustration of the A proposition, " All 
men are rational." Its contrary will be " No men are 
rational.'' ^ What exactly are the relations between 
these two propositions.? If A be true, it is obvious that 
E will be false, and if E be true A will be false. But 
if A be false, what about E.? It may be true or false, 
for the falsity of A leaves those two possibilities ; in 
other words, the truth or falsity of E is undetermined. 
Similarly of A, if E be false. If either be false, there is 
a middle ground; thus, it may be that some men are 
rational and some are not. Two propositions are con- 
trary when only one can he true and both can he false, 

"All men are rational" (A), and "Some men are 
not rational" (O), are contradictory propositions. If 
A be true, O will be false, and if A be false, O will be 
true ; likewise if O be true, A will be false, and if 
O be false A will be true. There is no middle ground ; 
there is no third possibility. Only one can be true, and 
only one can be false, or in other words, hoth cannot 
be true and hoth cannot be false. Two propositions are 
contradictory when they are exact opposites; one must 
he true and the other must he false. 

Of suh-contrary propositions, hoth may he true, hut 
only one can he false. The propositions, " Some men 
are rational " and " Some men are not rational," are 
in the relation of sub-contraries. If either be false the 
other must be true, and if one be true the other may be 
true also ; both may be true, and one must be. The 
propositions I and O are consistent, whereas contraries 
and contradictories are inconsistent. 

4 Two propositions which are to stand in a relation of op- 
position to each other must have identical terms. This is true 
in the traditional treatment, but exceptions will be noted later. 



116 VERIFICATION AND DEDUCTION 

In the case of subalterns, both propositions are of 
the same quahty, but they differ in quantity. "All 
men are rational " and " Some men are rational " are 
subalterns. If the universal be true the particular will 
of course be true also; but if the universal be false the 
other is left indeterminate ; it may be true or it may be 
false. On the other hand, if the particular proposition 
be false, the universal will necessarily be false too; if 
it is false that " Some men are rational," it cannot be 
true that " All men are " ; but if the particular be true 
it is by no means certain that the other will be. Thus, 
if we know that somo men are rational, that does not 
give us a right either to affirm or to deny that all men 
are rational ; in other words, the truth of the universal 
is left indeterminate. 

To summarize : contrary propositions are such that 
only one can be true, and both may be false. 

Contradictory propositions are so related that one 
must be true and the other must be false. 

Sub-contraries may both be true, but only one can 
be false. 

Subalterns may both be true or both false. The 
truth of the universal assures the truth of the par- 
ticular, but the falsity of the universal does not in- 
volve the falsity of the particular ; the falsity of the 
particular involves the falsity of the universal, but the 
truth of the particular does not assure the truth of the 
universal. 

Relations of Opposition among Propositions which 
have not Identical Terms. — These relations are most 
easily detected between propositions which have the 
same subject and the same predicate, but it is possible 



RELATIONS OF OPPOSITION 117 

to find them in propositions which do not answer to this 
description. The propositions, " All men are rational " 
and " All men are idiots," are contraries. Both cannot 
be true, but both may be false. 

Or again, ". Socrates was the wisest of the Greeks " 
and " Aristotle was the wisest of the Greeks," are con- 
trary propositions. Only one of them could be true, 
while both might be false. 

This will be found to be the case with a great many 
inconsistent propositions. In fact all inconsistent 
propositions which are not contradictories are con- 
traries. Many pairs of such inconsistent propositions 
would not fit into the square of .opposition, for both 
might be affirmative or both might be negative. A and 
E propositions which have identical terms are contra- 
ries : we need not consider the meaning of the proposition 
to discover that, for it is evident from their form. In 
other cases we must take into account the meaning as 
well. " A is B " and " A is not B " are contraries so 
long as the meaning of the terms A and B remains the 
same, no matter what that meaning is ; but the relation 
between " A is X " and " A is Y " can be determined 
only after we know the meaning of X and Y. If we 
learn that X and Y are opposites we can, of course, re- 
state our second proposition, "A is Y," in the form 
" A is not X," the contrary of " A is X." If X and 
Y prove to be the same or similar in meaning the two 
original propositions are of course consistent. 

Subject and predicate may both be different; e. g,y 
" Oxygen is heavier than nitrogen " and " Nitrogen is 
heavier than oxygen." Only one cannot be true ; both 
might be false. If two propositions, alike in quality, 



118 VERIFICATION AND DEDUCTION 

have the same subject but have predicates which are 
complete opposites, as X and not-X, the propositions 
will be contradictories. Such pairs of terms as " ra- 
tional and non-rational," " square and not-square," are 
examples. 

Cases sometimes occur in which propositions having 
the same predicates but different subjects will be con- 
tradictory in meaning: thus, " Man alone is rational "; 
" Some being besides man is rational." 

Similarly, propositions with unlike terms may stand 
in the relation of sub-contraries. For example : " Some 
men are rational " and " Some men are irrational," and 
" Simple substances make up a large part of the 
earth's crust " and " Compound substances make up 
a large part, etc.," are pairs of sub-contraries. 

And likewise in the case of subalterns : for example, 
" All men are vertebrates " and " All men are mam- 
mals " ; " No mental states can be weighed," " No emo- 
tions can be weighed." The relation of subaltern may 
hold between two propositions even if one of them is not 
universal. Thus, " Most books are worthless " and 
" Some books are worthless." Of course, " The recent 
novels are worthless," is not necessarily a subalternate 
of either of these propositions. 

Singular propositions require special notice. " Soc- 
rates was the noblest of men " and " Socrates was not 
the noblest of men " are apparently contrary propo- 
sitions, but as a matter of fact they are contradictories. 
Singular propositions which have the same terms are 
never contraries except in form. On the other hand, 
" Socrates was an Athenian " and " Socrates was a 
Spartan " are contraries. 

Conversion. — A proposition is the verbal expression 



CONVERSION 119 

of a judgment, and a judgment is an act of thought 
wherein we assert that certain relations hold among cer- 
tain objects of thought, as, A is B, A is not B, some A 
is Y, and so on. Now it is often possible to formulate 
other propositions which are equivalent to these or 
which are obviously true if the original proposition be 
true. The proposition, " No conic sections are rectan- 
gular figures," is equivalent to " No rectangular figures 
are conic sections." The only difference between the 
two is in the order of the terms. The original subject 
and predicate have been interchanged. This process 
is known as Conversion. The proposition just con- 
verted was an E proposition and all E propositions can 
be converted. 

Again, the proposition, " Some metals are elements " 
can be converted into " Some elements are metals." 
Both are I propositions. From the proposition, " Some 
quadrupeds are horses," we can get only " Some horses 
are quadrupeds." We happen to know that the same 
could be said of all horses, but we do not get that 
knowledge from the original proposition. The original 
statement is aflSrmative and affirmative propositions, as 
we have seen, do not give information about the whole 
of the predicate. But the statement, " All horses are 
quadrupeds," being universal, affirms something about 
the whole class horses. 

The first general rule of conversion is that no term 
may he distributed in the converse which was not dis- 
tributed in the original proposition, A proposition, 
then, such as " All *A propositions are universal," can 
have as its converse only an I proposition, " Some uni- 
versal propositions are A propositions." 

Each of the propositions dealt with above has had as 



120 VERIFICATION AND DEDUCTION 

its converse another proposition having the same 
quality. In all cases the converse of a proposition must 
have the same quality as the original proposition. This 
is a second rule of conversion. From this and the for- 
mer rule it follows that the O proposition can have no 
converse. Its subject is undistributed and its quality 
negative; but in the converse, the original subject, hav- 
ing become the predicate of a negative proposition, 
would be distributed, a violation of the first rule. 

Proposition Converse 

The converse of A is I; All S is P;^ Some P is S." 

The converse of I is I: Some S is P; Some P is S. 

The converse of E is E: No S is P; No P is S. 
O has no converse. 



The use of Euler's circles ^ will help to make these re- 

A (p:s) All S is P or (at least) some P is S. 
E (S) (P) No S is P or no P is S. 
I \ (S)P^' (At least) some S is P or some P is S. 
O (gfp)) Some S is not P but all P may be S. 
or no P may be S> or some 'may be and some 
may not be. 

lations clear. We see that propositions E and I are 
converted into E and I ; in technical language they are 
converted " simply." A can be converted only into I ; 

^ The forms here used are taken from Hyslop's Elements of 
Logic, 



OBVERSION 121 

that IS, it is converted into a proposition which is less 
general than itself, into a particular proposition. Such 
conversion is known as conversion by limitation or per 
accidens. 

Obversion. — Again, we may find for all ordinary 
propositions an equivalent of the opposite quality : " All 
men are wise " is equivalent to " No men are unwise '' ; 
" Some men are just " can be expressed as " Some men 
are not unjust " ; " No animals are moral " as " All ani- 
mals are unmoral " ; " Some men are not honest " as 
" Some men are dishonest." It will be noticed that in 
every case the subject is unchanged. (In " All men are 
wise," and " No men are wise, ' the subject is in both 
cases " All men " ; the " No " belongs to the statement 
as a whole, not to the subject. The negative of " All 
men " would be "All who are not men.") This process 
is called Obversion. The quality of the proposition is 
changed and the predicate of the obverse is the com- 
plete opposite of the predicate of the original proposi- 
tion. 

Proposition Obverse 

The obverse of A is E; All S is P; No S is not-P. 

The obverse of I is O: Some S is P; Some S is not not-P. 

The obverse of E is A: No S is P; All S is not-P. 

The obverse of O is I: Some S is not P; Some S is not-P. 

If the predicate in the original proposition be nega- 
tive, as non-conductor, it will be replaced in the obverse 
by the corresponding positive term, conductor. '^ Some 
S is not-P " will have as its obverse " Some S is not 
P." Difficulty is likely to arise with regard to the 
predicate and its opposite. For example, the proposi- 
tion, " No animals are moral," is not equivalent to " All 



122 VERIFICATION AND DEDUCTION 

animals are immoral." They may be neither moral nor 
immoral. The predicate in the new proposition must 
be completely opposite or contradictory to the original 
predicate. Sometimes it can not be expressed simply. 
For example, take the proposition, " The president is 
the nation's highest executive ofBcer." In the obverse 
the whole of the predicate must be made negative, not 
simply " highest " or " executive " or " officer." It 
might read, " The president is not any one who Is not 
the nation's highest executive officer." 

The following symbols may be employed to indicate 
the relations considered in obversion. Suppose we have 
a proposition with the predicate P or not-P. Every- 
thing in the universe either has or has not the predicate 
P, that is, everything has one or the other of the 
predicates P and not-P. We may represent this fact by 
a circle divided into two compartments, thus : 




m^ 



Then any given thing will fall into one or the other of 
those compartments. If our proposition asserts that 
it falls^ into one, that is tantamount to asserting that it 
falls outside the other; the latter assertion would be 
the obverse of the former. S is P, implies that S is not 
not-P ; T is not-P, imphes that T is not P. 

Contraposition. — These changes in the form of prop- 
ositions may both be present together and repeatedly. 
Let us take the proposition, " No men are immortal." 



CONTRAPOSITION 123 

The obverse would be, " All men are mortal '' ; the con- 
verse of this, " Some mortals are men " ; the obverse of 
this again, " Some mortals are not not-men " (not 
anything else than men) ; and this, being an O propo- 
sition, has no converse. We might, of course, have 
begun with conversion. 

What is known as Contraposition is equivalent 
to obversion plus conversion.^ The contrapositive of 
" No men are immortal " is " Some mortals are men " ; 
the contrapositive of " All men are mortal " would be 
" No immortals are men." In the contrapositive the 
subject is the opposite of the original predicate, the 
predicate is the original subject, and the quality of the 
proposition is the opposite of that of the original prop- 
osition. An application of the rules for conversion will 
show that the I proposition has no contrapositive. The 
contrapositives of the various propositions are as fol- 
lows: 

Proposition Contrapositive 

A, contrapositive E: All S is P; No not-P is S. 
I, no contrapositive. 

E, contrapositve I: Ko S is P; Some not-P is S. 

O, contrapositive I: Some S is not P; Some not-P is S. 

In Conversion, Obversion, and Contraposition we 
have found certain variations in the forms in which a 
given thought content can be expressed. Such varia- 
tions in the form of expression help to make clearer 
just what the content of the judgment really is. In 
these processes the changes in the form of expression 
are due to a change in the order of subject and predi- 

6 Some logicians add a second obversion. See Hibben, Logic. 



124 VERIFICATION AND DEDUCTION 

cate or a change in the quality of predicate and copula, 
or both. 

EXERCISES 



1. Give contrary^ contradictory^ and subaltern of each of 
the propositions in Exercises '' 5/' pages 62-65; where it is 
not possible to give all^ state the reason why. 

2, Classify the subjoined propositions into the four fol- 
lowing groups: 

1. Those which can be inferred from (1)* 

2. Those from which (1) can be inferred. 

3. Those which do not contradict (1) but cannot be 

inferred from it. 

4. Those which contradict (1). ^> 



(10 

(11 
(12 

(13 

(14 



of each o 

(1 

(2 
(3 

(4 

(5 
(6 

(7 



j|M 



\ 



\^^ 



/ 



All just acts are expedient acts. 

No expedient acts are unjust. 

No just acts are inexpedient. 

All inexpedient acts are unjust. 

Some unjust acts are inexpedient. 

No expedient acts are just. 

Some inexpedient acts are unjust. ^ 

All expedient acts are just. 

No inexpedient acts are unjust. 

All unjust acts are inexpedient. 

Some inexpedient acts are just acts. 

Some expedient acts are just. 

Some just acts are expedient. 

Some unjust acts are expedient. (Jevons.) 



JN;' 



^ 



;-V 



.«* 



\' 



^' 



3. Give the converse^ the obverse^ and the contrapositive 



f the following propositions : 

All who were present were unprepared. 

No wise man would undertake such a task. 

Not to make the attempt is to confess yourself 
a coward. 

Charity begins at home. 

No statesman could have stooped to such a deed. 

Only a fanatic believes in panaceas. 

Discontent is frequently a symptom of ineffi- 
ciency. 



EXERCISES 125 

(8) A revolution is a surgical operation which self- 

appointed healers of social diseases are very 
ready to recommend as a preliminary to every 
cure. 

(9) Uneasy rests the head which wears a cro^s^^n. 

(10) All organic substances contain carbon. 

(11) Better late than never. 

(12) Not many of the metals are lighter than water. 
4. State the relation of each of the following proposi- 
tions to the succeeding one: 

(1) All the metals are elements. 

(2) No metals are non-elements. 

(3) No non-elements are metals. 

(4) All non-elements are not-metals. 

(5) All metals are elements. 

(6) Some elements are metals. 

(7) Some metals are elements. 

(8) No metals are elements. (Hyslop.) 






K7 



r 

CHAPTER VIII ^ 
THE SYLLOGISM 



The Principles of Syllogistic Reasoning. — Let us re- 
turn to the examination of the syllogism. Every com- 
plete syllogism contains three propositions and only 
three. They are a major premise, a minor premise and 
a conclusion. In the syllogism, " All men are mortal ; 
Socrates is a man ; therefore Socrates is mortal," the 
first proposition is the major premise, the second is the 
minor premise, and the third is, of course, the conclu- 
sion. The major premise is the broad foundation on ' 
which the reasoning rests. It is a universal proposi- j 
tion in syllogisms of this form,. It may be either affirm- 
ative or negative. Thus we may have, " No men are 
immortal ; Socrates is a man ; therefore Socrates is not 
immortal.'' The major premise asserts that the whole 
of a certain class is included in another class or excluded 
from it, or it assigns a certain predicate to the whole 
of a certain subject.^ The minor premise asserts that 
certain things are included in the first class ; and the 
conclusion applies to these things the assertion which 
was made about the first class. 

* This chapter may be omitted. The traditional treatment is 
given in chap. ix. 

1 We have seen that all propositions may be regarded as stat- 
ing a relation between classes, and that this way of regarding 
them is most useful and convenient. But other types of rela- 
tions between subject and predicate exist and should not be 
forgotten. 



THE FIRST FIGURE 



127 



Behind this reasoning lies the principle called the 
Dictum de Omni et Nullo; i. e,, " Whatever state- 
ment may he made with regard to a class taken gen- 
erally may he made of each and every memher of that 
class,'''' or " Whatever is true of each of the members 
of a class will be true of everything found to be a 
member of that class." 

The application of this principle in the two syllo- 
gisms employed for illustration is perhaps obvious, but 
it may be well to represent the relation of the various 
terms graphically. For this purpose Euler's diagrams 
are valuable. 






The class men is first included in the class mortal ; 
the individual Socrates is then included in the class 
men and must in consequence be included in the class 
mortal. In the second case men is excluded from im- 
mortal and hence Socrates, who is included in men, will 
necessarily be excluded from immortal. 

It will readily be seen that (1) the minor 'premise in 
a syllogism of this sort cannot he negative, A nega- 
tive minor premise would assert that something did not 
belong to the class indicated by the subject of the major 
premise, and would give no ground for a further con- 
clusion. The fact that something is true of a whole 
class of objects does not tell us whether it will or will 



128 



THE SYLLOGISM 



not be true of some things not included in that class. 
Thus the premises, " All men are rational beings ; 
monkeys are not men/' do not v/arrant the conclusion 
that monkeys are not rational.^ Other conclusions are 




possible and we could not prove this one without using 
information not contained in our premises. If we tried 
to prove it by those premises alone, our reasoning 
would be invalid. An invalid syllogism is one in which 
the conclusion is not proved or made necessary by the 
premises. The conclusion may be true, but the func- 
tion of the syllogism is to furnish a conclusion which 
must be true if the premises are true. Reasoning which 
does not prove the conclusion is fallacious, or in other 
words, it contains a fallacy. 

We have seen that the minor premise In a syllogism of 
this form cannot he negative. It will be obvious that 
(2) if the major premise he affirmative the conclusion 
must he affirmative and that if the premise he negative 
the conclusion must he negative. If we affirm something 
of a whole class we cannot deny it of a part of the 

2 These diagrams may be employed in illustrating the later 
rules also. 



THE SECOND FIGURE 129 

class, and if we deny it of the whole class we cannot 
assert it of a part. It is true also that (3) the major 
premise cannot he particular. If we have the premises, 
''Some animals can be domesticated; the wolf is an 
animal/' we are obviously not justified in concluding 
that the wolf can be domesticated. 

And again (4) i/ the minor premise he particular^ the 
conclusion cannot he universal; it must be particular 
too. From the premises, " All works of art are valu- 
able; some of the objects in this collection are works 
of art," we cannot conclude that all the objects in this 
collection are valuable. In no case can our conclusion 
contain more than was contained in the premises. 

Syllogistic Proof, — In examining syllogistic reason- 
ing the first question is not " Is the conclusion true? " 
but " Does the conclusion follow necessarily from the 
premises? " If the syllogism of this form correctly 
applies the Dictum de Omni et Nullo the reasoning is 
valid. A syllogism of this form is said to be in the 
First Figure, and this is the only form of syllogism 
which can be used to prove a universal affirmative prop- 
osition. 

A Second Type of Syllogism. — There are sev- 
eral other varieties of syllogisms, each having certain 
special principles of its own. The one next to be dis- 
cussed is used to prove that two facts or groups of 
facts are not the same ; it proves negative conclusions 
and only those. Its Principle is this : if one of two 
things is included in a class from which the other is 
excluded,^ these things are excluded from each other. 
To illustrate : " Every college-bred man has read that 

3 Or if one has a predicate which the other lacks. 



130 THE SYLLOGISM 

book; this man has not read the book; therefore, this 
man is not college-bred." The fact that two subjects 
are included in the same class or that they possess the 
same predicate does not, on the other hand, prove that 
they are the same or that they are related in any other 
way. They might be even identical, it is true, but in 
the conclusion of a syllogism we are entitled to include 
only what must he. 

Special rules, — In this sort of syllogism (1) no conn 
elusion can he drawn from two affirmative premises. 
Either of the premises may be negative and one of 
them must be. In the illustration given above, the 
minor premise was negative. We might have " No col- 
lege man would do this deed ; this man has done it ; 
therefore, he is not a college man." 

On the other hand (2), hoth premises can not he 
negative; only one may he negative. If two things 
both lack the same predicate that fact alone does not 
warrant any further statement. " No Indians are Cau- 
casians " and " No Chinamen are Caucasians " does not 
furnish any basis for a statement concerning the rela- 
tion between Indians and Chinamen. 

(3) The major premise in a syllogism of this sort 
must he universal. If our major premise were " Some 
college men are informed upon this subject," it would 
be possible that some were not, and the fact that a 
given man was ignorant of it would not prove that he 
was not a college man. 

(4) The minor premise may he either universal or 
particular; if it is particular, the conclusion must be 
particular; if it is universal, the conclusion may he uni- 
versal. It is obvious that if we make a statement about 
only a part of the class for which the subject of the 



MAJOR AND MINOR PREMISES 131 

minor premise stands, we cannot make a statement 
about the whole of it in the conclusion. In every syllo- 
gism, the information contained in the conclusion must 
be furnished in the premises. 

Major and Minor Premises, — It is not always easy 
to know immediately which is the major premise in a 
syllogism of this form. There is, however, a rule which 
can be applied to all syllogisms. The major premise 
is the one which contains the major term. The major 
term is the predicate of the conclusion. In an affirm- 
ative conclusion the subject may be regarded as con- 
tained in the predicate. In the proposition, " All 
triangles are geometrical figures," the class triangje 
is included in the class geometrical figures. The latter 
term is the major because it stands for the wider class. 
In negative propositions, the predicate is not neces- 
sarily wider ; in the proposition, " No conic sections are 
triangles," the predicate is not wider than the subject. 
Still, for the sake of uniformity, the predicate of the 
conclusion is always called the major term. The syllo- 
gism first discussed is a syllogism in the First Figure 
and the other is in the Second Figure, 

The Third Figure. — In the next type of syllogism, 
the subject is the same in both premises, but the predi- 
cates are different, or in other words, the subject is 
related by inclusion or exclusion to one class in the 
major premise and to another in the minor premise. 
The Principles of the Figure might be stated as follows : 
1, If a class (or individual) is included in 
each of two other classes those classes include 
each other, at least in part. All X is Y and 
all X is Z ; therefore, some Z is Y. 

2. // a class {or individual) is excluded from a 




V 




132 THE SYLLOGISM 

second class and included in a thirds then a 
r^part, at least, of the third is excluded from the 

second. No X Is Y and all X Is Z; therefore, 
some Z is not Y.^ 

In some cases a conclusion Is possible If only a part 
of the subject Is described In one of the premises. 
Some of the special rules which follow state the condi- 
tions In which this is true. (1) One of the premises 
must be universal. For example, " No precious metals 
are soluble in sulphuric acid ; some precious metals are 
soluble In nitric acid ; therefore, some things soluble In 
nitric acid are not soluble In sulphuric acid." If the 
first makes an assertion about only a part of the class 
and the second likewise, we can not be certain that the 
two parts are the same and thus we learn nothing about 
the relation of their predicates. Thus, " Some triangles 
are scalene " and " Some triangles are right-angled " 
are premises which warrant no conclusion regarding the 
relation of scalene to right-angled figures. (2) The 
major premise in this Figure may be either affirmative 
or negative. The conclusion will have the same quality 
as the major premise. If " No A is B," and " Some (or 
all) A is C," then " Some C is not B " ; or if " All A is 
B," and " Some A Is C," then " Some C Is B." (3) The 
minor premise can not be negative. If " All deer are 
herbivorous," and ^ ' No deer are hollow-horned ani- 
mals," we cannot conclude that " No hollow-horned 
animals are herbivorous." (4) The conclusion of a syl- 
logism in the Third Figure is, in all cases, particular. 
From " All men are mammals " and " All men are bi- 

4 The student should test each of the special rules by the use 
of such diagrams. 



THE FOURTH FIGURE 133 

peds " we can not conclude that " All bipeds are mam- 
mals." The fact that some or all of a certain class are 
Included in another class or possess a given predicate 
(the minor premise asserts this) does give us infor- 
mation about a part of that predicate, but not about 
the whole (it does not distribute the predicate) ; as 
that predicate becomes the subject of the conclusion, 
the conclusion must be a particular proposition. 

The Fourth Figure. — The three figures already dis- 
cussed were described by Aristotle. The fourth is the 
invention of later logicians and is usually regarded as 
much less important than any of the others. In it the 
minor premise states something about the predicate of 
the major premise, and the conclusion in turn states 
something about the conclusion of the minor premise. 
Thus, " All great poems are the products of genius ; 
all the products of genius are inimitable ; therefore, some 
inimitable things are great poems." (If the conclu- 
sion were, " Great poems are inimitable," we should have 
a syllogism of the First Figure, and " All the products 
of genius, etc.," would be the major premise). The 
Principles of this Figure are: 1. If a class is included 
in a second class and this in turn is included in a third, 
then the third will be partly coextensive with the first. 

All X is Y 
All Y is Z 




Some Z is X 

2. If a class is excluded from a second and the lat- 
ter is included in a third, then a part, at least, of the 
third will be excluded from the first. 



134 THE SYLLOGISM 




No Y is X 
All X is Z 



Some Z is not Y 




3. If a class is included in a second and the latter is 
excluded from, a third, then the third will be excluded 
from the first. 

All X is Y 
,x^ No Y is Z 

No Z is X 

In the illustration we have used it is obvious that we 
can not conclude that " All inimitable things are great 
poems.'' Our minor premise has not given us any in- 
formation about the whole of the class, " inimitable 
things," so we can not have a universal conclusion in 
this instance. If our syllogism were, " All great poems 
are the products of genius ; some products of genius 
are inimitable," it would be impossible to draw a con- 
clusion. Poems might not happen to belong to the 
things included in the minor premise. The result would 
be similar if the minor premise were " Some products 
of genius are not inimitable." If the minor premise 
were, " No products of genius are inimitable," we could 
of course conclude that no inimitable things were poems. 
We can formulate this rule: (1) // the major premise 
be affirmative the mi/nor premise must be universal. In 
all these instances, the major premise was the same and 
it was universal. Suppose we had " Some great poems 



THE FOURTH FIGURE 135 

were the products of genius." It will be seen that the 
minor premise, " All works of genius, etc.," will give a 
valid conclusion, but that none of the others will. 
(2) // the major premise he affirmative and particular, 
the minor premise must be universal and affirmative. 
With the minor premise " No products of genius are 
Inimitable," no conclusion can be drawn : since only 
some great poems have been included in w^orks of 
genius, it may well be that some Inimitable things may 
be found among those not so included. (3) The major 
premise may he negative, " No great statesmen are 
selfish politicians ; some (or all) selfish politicians amass 
great fortunes ; therefore, some persons who amass 
great fortunes are not great statesmen." Some such 
persons might be great statesmen, so far as our pre- 
mises are concerned; hence we have no right to con- 
clude that no persons who amassed great fortunes were 
great statesmen. 

EXERCISES 

State the Figure and point out the errors in reasoning in 
the following syllogisms: ^ slY' 

(1) All wisdom is desirable^ but a knowledge of 

slang is not wisdom^ and is, therefore, not ^ -^ 
desirable. , i^ 

^ (2) Logic and mathematics furnish good mental , 

training, and consequently the latter may be . -^v^^ 



^/^' 



regarded as a branch of the former. ^^iS 

(3) Some athletes are susceptible to pneumonia, and ^ 

as all these men are athletes some of them 
must be susceptible to pneumonia. 

(4) Some industrious people are also bright, for there 

are both bright and industrious students in ^"^ 
^ that group. 
V 



p ,. 

\ 136 THE SYLLOGISM 

\ J. 

'^-^"""^ (5) Some statues are very lifelike^ and no lifelike 
things are contrary to the laws of nature; 
hence^ nothing contrary to the laws of nature 
is a statue. 

(6) Some gymnastic exercises are good for increasing 

strength^ but swimming is not_, and hence is 
not a gymnastic exercise. 

(7) All Democrats voted against the bill^ and as 

most of our Congressmen are Democrats^ they 
must all have voted against the bill. 

(8) All M is P; 
No M is S; 

.'.No S is P. 

(9) Europeans cannot endure that climate; neither 

can Americans; hence^ Americans may be re- 
garded as a species of European. 

(10) All ballads are interesting^ and some interest- 

ing things are very old; hence^ some very old 
things are ballads. 

(11) All text-books are to be had at this store^ but 

some novels are not to be had here^ which 
proves that novels are not text-books. 
For further examples see page 150 and page 177f. 




A 



o 



v»s^ " C-" 






O 



if 



.sl-'-'^-"*' '.>^«-^, 



"(Fv./ x; 



/i/^< /'"f <? " '^ 



A 



t' 



A 





^ 



X^RN. 



The traditional treatme^of the sf^gism is sim- 
ple though very formal. The syllogism is regarded as 
a form of reasoning in which each of two terms is 
compared with a third and as a result the two terms 
are found to be related to each other. Each of the 
two is compared with the third in a 'premise. The re- 
sult of the comparison is stated in the conclusion, 

(M) is P ) 

/-\ . ^\ Premises. 

@ IS M ) 

S J is P Conclusion. 




P and S are found to stand in certain relations to M. 
In this case and in many others we are justified in as- 
serting a relation between S and P ; S and P are found 
to be related through M as a medium. For this rea- 
son M is called the Middle Term and the syllogism is 
said to embody Mediate Reasoning, 

The validity of the reasoning is tested by the appli- 
cation of a number of rules. These rules have to do 
with the relation and distribution of the several terms 
in the syllogism. They are as follows: 

1. Every syllogism contains three propositions and 
only three. 

2. Every syllogism has three terms and only three. 
(If any term is ambiguous this rule is violated.) 

137 



138 TREATMENT OF THE SYLLOGISM 

3. The middle term must be distributed at least 
once. 

4JiNo term may be distributed in the conclusion which 
was n^^istributed in one of the premises. 

5. From- two negative premises nothing can be in- 
ferred. 

6. If one premise be negative, the conclusion must 
be negative ; if both premises be affirmative, the con- 
clusion must be affirmative. 

7. From two particular premises no conclusion can 
be drawn. 

8. If one premise be particular, the conclusion must 
be particular. 

Let us examine these rules in the order given. 

1. With more than three propositions, we should have 
more than a syllogism, though our reasoning might be 
valid. 

2. The violation of rule two gives rise to the Fallacy 
of Four Terms, Unless two of the terms are confused 
this fallacy is not likely to arise. No one would try 
to draw a conclusion from the propositions, " Socrates 
was a philosopher," and " The earth revolves about the 
sun." But one might be tempted to draw a conclusion 
from the premises, " Steel is made from iron ; iron is 
dug from the ground." Still, it would be wrong to con- 
clude that steel is dug from the ground. The terms 
here are, " steel," " (something) made from iron," 
"iron," and " (something) dug from the ground." 

3. The violation of rule three gives rise to the Fal- 
lacy of Undistributed Middle. Thus, the premises, 
" Some men are brave ; and some men are strong," do 
not prove anything ; nor do these ; ^ ■ All brave men 



THE UNDISTRIBUTED MIDDLE 139 

should be respected; and, all just men should be re- 
spected." 1L 

Let us represent the middle term by M, the minor 
term (subject of the conclusion) by S, an^ the major 
term (predicate of conclusion) by P. We are not jus- 
tified by the premises in making any statement about 
the relation of S and P, for they may be wholly or 
partially identical or they may be mutually exclusive. 
But if the middle term were distributed we might be 
able to draw a conclusion. If all M is P and all S is M, 
we may conclude that all S is P. 




Or if no M is P and all S is M, then no S is P. 




An invalid syllogism is one in which it is not possible 
to determine fully the relation of the circles to each 
other, since there are conflicting possibilities. In the 
case of Undistributed Middle cited above, all, some, or 
none of S may be included in P. 





140 TREATMENT OF THE SYLLOGISM 

In valid syllogisms there may sometimes be a margin 
of indefiniteness (owing to the indefinite character of 
the "particular" propositions), but a certain amount 
of definite information regarding the relation of S and 
P is always given and the relation of the circles sym- 
bolizing major and minor terms is not left wholly in 
doubt. 

The reason for the rule requiring the distribution of 
the middle term may he stated in this way: If each of 
two things is related to a part of a thirds we can not 
conclude that they are related to each other, for they 
may not he related to the same part; but if one {or 
both) is related to the whole of the third, then it may 
be possible to assert a relation between the two. Thus : 





All M is P 
All S is M 
All S is P 



© 



No M is P 
All S is M 
No S is P 




All P is M 
All S is M 
No conclusion. 




My 

Some M is P 

All S is M 
No conclusion. 



and so on 



4. The reason for rule four is obvious : if we know 
something about only part of a class in the premise, 



ILLICIT MAJOR AND MINOR 141 

we can not say something about all of it in the con- 
clusion. The violation of this rule gives rise to two 
fallacies : the Illicit Process of the Major Term and the 
Illicit Process of the Minor Term, In the syllogism, 
"All men (M) are vertebrates (P) ; all men (M) are 
rational (S) ; therefore, all rational beings (S) are 
vertebrates (P)/' we have an illustration of the Illicit 
Process of the Minor Term, or Illicit Minor, as it is 
usually called. In the syllogism, " All Chinamen (M) 
are Mongolians (P) ; no Japanese (S) are Chinamen 
(M) ; therefore no Japanese (S) are Mongolians (P),'' 
the Illicit Process of the Major Term occurs. Using 
the circles, we have for the first: 




and for the second: 




The dotted lines indicate possible boundaries of S. 

The premises do not justify us in including all of S 
within the circle P in the first, nor of excluding all P 
from the circle S in the second. S may be outside of 
M, but still be wholly or partially within P. 

5. With two negative premises, both major and 



142 TREATMENT OF THE SYLLOGISM 

minor terms are excluded from the middle term, but 
that does not tell us whether they are or are not ex- 
cluded from each other. 

6. With one negative premise, either major or minor 
term is excluded from the middle term, while the other 
is not ; therefore, if any relation can be asserted be- 
tween major and minor terms, it must be one of ex- 
clusion. 

7-8. The reasons for the two last rules can be more 
easily understood after we have considered the Moods 
and Figures of the syllogism. It will then be seen 
that the violation of these rules means a violation of 
rule three or rule four or both. 

The Figure of a syllogism is determined by the posi- 
tions of the middle term.^ 

r 

The Four Figures are as follows: 

1. M is P 2. P is M S. M is P 4. P is M. 
S is M S is M M is S M is S 



.*.S is P .*.S is P .'.S is P .*.S is P 

In the First Figure, the Middle Term is the subject 
of the Major Premise and the predicate of the Minor 
Premise. 

In the Second Figure it is the predicate of each. 

In the Third Figure it is the subject of each. 

In the Fourth Figure it is the predicate of the Major 
Premise and the subject of the Minor Premise. 

The position of the Middle Term in the Third Figure 

1 We have already seen that the Figures differ in other ways, 
but the traditional mode of distinguishing them is the one 
just mentioned. 



THE MOODS OF THE SYLLOGISM 143 

is the opposite of that which it occupies in the Second ; 
and in the Fourth it is the opposite of that in the First. 
The Mood of a syllogism is determined by the quan- 
tity and quality of the several propositions which it 
contains. Propositions, as we have seen, are of four 
kinds with respect to quantity and quality, and are 
represented by the four letters, A, E, I, and O. The 
letters AAA would symbolize a syllogism in which each 
proposition was a universal affirmative. There are 
sixty- four possible moods : 

AAA ABA ALA AOA EAA BBA BIA SOA 

AAB AEE Am AOB EAE BBS BIB EGE- 

AAI AEX- AH -AOt ^BAi- SSi- -BK -BOt 

AAQ- AEG -AiQ-^ AGO BAG BBO- BIG BOG- 

i4A ffiA- HA -lOA- ^OAA OBA GIA GOA 

-lAB -IBB -HB- -^tOB- -GAB OBB GBB OGB 
lAI 4BI- -Ht -i&L- -QAl OBI^ OH- GGI- 
■lAO- (lEG)-HG- iOe- GAG GE^ GiO GG0 . 

Many of these are at once seen to be invalid : thus, ap- 
plying the rules for negative and particular premises, 
we can eliminate those moods through which a line is 
drawn. The mood lEO does not violate any of those 
rules, but examination will show that it will give a fal- 
lacy of Illicit Major in each of the Figures. The con- 
clusion is negative and hence distributes its predicate, 
the major term. The major premise is an I proposi- 
tion and hence distributes neither of it§ terms ; there- 



144 TREATMENT OF THE SYLLOGISM 

fore, the major term can not be distributed in the 
premise, and hence this mood may be ehminated 
also. 

There remain only eleven moods which may be valid, 
but many of those are invalid in some of the figures. 
We will examine each of these moods in each of the 
figures.^ 

In the First Figure we should have the following re- 
sults : 



A.Qvl)-E 
A.(S>M 

a.CDp 
a.(m)-p 

I. S -M 

I. S -P 

e.(m)x0 

I. S -M 
O. Sx(p) 






It is evident that the following are invalid in the First 
Figure: AEE, AEO, AOO, lAI, and OAO. lAI and 
OAO are invalid because of an Undistributed Middle, 
the others because of Illicit Majors. 

The valid moods are AAA, AAI, All, EAE, EAO, 
and EIO. AAI and EAO are necessarily valid since 
AAA and EAE are valid. I and O are called weakened 
conclusions because they are less general than they 



2 To facilitate dealing with them we shall employ the S3rmbols 
used in the exposition of Conversion and Obversion. 



THE SECOND FIGURE 



145 



might be. A comparison of these moods will show that 
two general statements may be made regarding reason- 
ing in this figure: 

1. The Major premise must he universal. 

2. The minor premise must he affirmative. 

Examination of the illustrations given in the pre- 
vious discussion of this Figure (page ) will show 
that every syllogism which violated either of these two 
rules failed to give a valid conclusion. 

In the Second Figure the results are different : 





I. S -M 
O.Sx(P 




A.gp;- M 

O. Sx@ 

o.sxd; 




A.(P)-M A.(?)-M 

E.(Dx(g) E.(s)x@ 
E.(i)x(P) O.Sx(P 




E.(P)x® E.(P)x(M) 
A.(S)- M A.(S)- M 
E.(S)x(p) O. S x(P 



Here the moods, AAA, AAI, AH, lAI, and OAO are 

invalid, the last because of Illicit Maj or, the others be- 
cause of Undistributed Middle. 

The valid moods are AEE, AEO, AOO, EAE, EAO, 
and EIO. O is a weakened conclusion in AEO and 
EAO. Here we find that in the Second Figure: 



146 TREATMENT OF THE SYLLOGISM 

1. The major premise must he universal, 2. One prem- 
ise must he negative and the conclusion likewise must 
be negative. 

These rules^ like those of the First Figure, might 
have been formulated on the basis of the typical cases 
presented in the earlier discussion. (See p. 130.) 

Again in the Third Figure : 








a.(m;^p 

A.(M)-S 
1. S -P 

A.(M)-P A. 
J. M -S CM 

I. S -P O. 

E.(M>(p) r. M -P 

L M -S A.@-S 
O.Sx(P) I. S -P 

In this case the invalid moods are AAA, AEE, AEO, 
AOO, EAE. Of these, AAA and EAE are cases of 
Illicit Minor; and the rest, of Illicit Majors. The 
vahd moods here are AAI, AH, EAO, EIO, lAI, and 
OAO. In the Third Figure : 

1. The conclusion must he particular, 

2. The minor premise must he affirmative. 

In this case, as in the others, the rules might have 
been discovered, without consideration of the moods, by 
a direct examination of cases. 



:ej™^ e.(m)' 
E.^m) o. 

e.(mKp) 

A.@-S 
O. Sx(P 

0.,M5<p) 

.A.(M)-S 

o. sxrp 



THE FOURTH FIGURE 



147 



In the Fourth Figure we have: 




A.(p;-M 

A.@-S 
I. S -P 



A.(P)-M 
E.@x(S 

E.(s)xrp 





E(P>@ 
I M -S. 
O.Sx(P) 



I. P -M 
A@-S. 

I. S -P 




A.(P)-M. 

E.(M)x@ 

O.Sx@ 

E.(g)xi 



A(M)-S. 
O.SxfP 



Here the invalid moods are AAA, AH, AOO, EAE, and 
OAO. AAA and EAE give lUicit Minor, AH and AOO 
give Undistributed Middle, and OAO gives Illicit Ma- 
jor. The valid moods are AAI, AEE, AEO, EIO, lAI. 
We get these rules for the Fourth Figure : 

1. If the major premise he affirmative, the minor 
premise must he universal. 

2. // the major premise he also particular, the minor 
premise must he affirmative. 

S. If the minor premise be affirmative, the conclusion 
must he particular. 

4. // either premise he negative, the major must he 
universal. 

5. The conclusion may not he a universal affirmative 
proposition. 



148 TREATMENT OF THE SYLLOGISM 

Comparison of all the valid moods shows that the 
mood AAA is valid in the First Figure only. As this 
is the only mood in which A appears as a valid con- 
clusion, it will be evident that a universal affirmative 
conclusion can be proved in the First Figure only. 



REDUCTION OF THE MOODS AND FIGURES. 

The Medieval schoolmen invented a set of menemonic verses 
to serve as an aid to the memory in recalling the valid modes in 
the several Figures. The verses consisted of barbarous Latin 
terms. The words contain also letters for guidance in reduction 
of the other Figures into the First. These verses, with their 
interpretation, are as follows: 

Barbara, Celarent, Uarii, Ferioque prioris; 
Cesare, Camestres Fesiino, Baroko secundae; 
Tertia, Darapti^ Disamis, Datisi^ Felapton, 
Bokardo, Ferison, habet, quarta insuper addit 
Bramant/p, Camenes; Dimaris, Fesa^o, Fresison, 

The moods are indicated by the italicised letters. All the 
valid moods are included except those in which there are so- 
called weakened conclusions, i. e,, cases in which a particular 
conclusion is drawn, though a universal would be valid, such as 
AAI or EAO in the First Figure. The first line indicates the 
moods of the First Figure, the second line, of the Second, the 
third and the first half of the fourth indicate those of the 
Third Figure, and the last line, those of the Fourth Figure. 

The First Figure was regarded as the Perfect Figure, and the 
others were transformed into it by making certain changes in 
their various members. This process was called the Reduction 
of the Imperfect Figures. These words contain letters which 
stand for the changes which must be made. The capital letters 
in the last four lines indicate the mood of the First Figure to 
which the mood, indicated by the word in which they are found, 
may be reduced. Thus Cesare may be reduced to Celarent. 
p indicates that the preceding proposition is to be converted 
per accident or by limitation; s indicates that the preceding 
proposition is to be converted simply, and m indicates that the 
premises are to be transposed. 



Camestres 
All A is C 

(All stars are suns) 
No B is C 

(No planets are suns) 
Therefore, B is not A 

(No planets are stars) 



Celaren^t 
C is not B 

(No suns are planets) 
All A is C 

(All stars are suns) 
Therefore, no A is B. 

(No stars are planets) 



REDUCTION OF THE FIGURES 149 

The minor premise in Camestres is first converted, then the 
two premises are transposed, and finally the conclusion is con- 
verted. To reduce Cesare to Celarent we need only convert 
the major premise. 

As a second example we may take the reduction of Bramantip 
to Barbara. 

Bramantip -^ Barbara 

All C is B All B is A 

All B is A All C is B 

Some A is C All C is A ^ 

In this case, the premises are transposed, and the conclusion 
is converted. This would give AAI. But the conclusion A would 
be valid from these premises. The p in this case may be taken 
as indicating that, instead of a conclusion less in quantity than 
the original proposition, we may have one which is greater in 
quantity, namely, universal. 

There is one more significant letter in these words, the letter 
k. It indicates that the reduction must be made by indirect 
means. Take, for example, Bokardo which reduces to Bar- 
bara. 

BoKARDO Barbara 

Some A is not C All B is C 

All A is B All A is B 

Therefore, some B is not C Therefore, all A is C 

In this case the major premise of Bokardo is the contradictory 
of the conclusion of Barbara; and the conclusion of Bokardo 
is the contradictory of the major premise of Barbara. Suppose 
the conclusion of Bokardo to be false; then its contradictory, " All 
B is C," will be true; taking this as the major premise of a new 
syllogism and the proposition, " all A is B," as the minor pre- 
mise, the conclusion will be the contradictory of the major premise 
of Bokardo and the new syllogism will be in the mood Barbara. 
Bokardo may be also be reduced to Darii. First obvert, then con- 
vert, the major premise; transposing the two premises, we then 
have Darii. All this mechanism is entirely unscientific and its 
interest is purely historical. 



I i 



EXERCISES ON THE SYLLOGISST 



1. What kinds of propositions are incapable of proof in 
the Second^ Third and Fourth Figures respectively? Give 
the reasons for your reply. 

2. If either premise of a syllogism is O^ what must the 
other be? 

3. With I as the major premise^ what must the minor 
premise be? 

V 



150 TREATMENT OF THE SYLLOGISM 

4. Show that an E proposition is highly efficient as a 
major premise. (J.) ^ 

5. Show that O is seldom admissible as a minor premise. 

(J.) 

6. Prove that there must always be in the premises one 
more distributed term than in the conclusion. (J.) 

7. Prove from the general rules of the syllogism^ that 
when the major term is the predicate in its premise_, the 
minor premise must be affirmative. (J.) 

8. Point out which of the following pairs of premises 
will give a syllogistic conclusion^ and name the obstacle 
which exists in other cases. 

(1) No A is B; some B is not C. 

(2) No A is B; some not C is B. 

(3) All B is not A; some not A is B. 

(4) Some not A is B ; no C is B. 

(5) All not B is C; some not A is B. 

(6) All A is B; all not C is B. 

(7) All not B is not C; all not A is not B. 

(8) All A is not B ; no B is C. 

(9) All C is not B ; no A is not B. 

3 (J) refers to Jevons, Studies in Deductive Logic, where 
a great many more questions of this character may be found. 
The following exercise is from the same source. 



V 




CHAPTER X 

ABBREVIATED AND COMPLEX FORMS OF 

REASONING — HYPOTHETICAL AND 

DISJUNCTIVE SYLLOGISMS 

The Enthymeme. — Usually our reasoning does not 
fall into the form of a perfect syllogism. In the first 
place it very often happens that one or another of the 
propositions is omitted. For example, " This object 
can be magnetized, for it is made of iron," omits the 
major premise, " All things made of iron can be mag- 
netized." Again, in " Every member of the jury voted 
for acquittal, therefore X voted for acquittal," the 
minor premise, " X was a member of the jury," is 
omitted. In " All metals are elements ; this is a metal," 
the conclusion is omitted. 

Syllogisms from which one proposition is missing are 
called Enthymemes. The missing premise can usually 
be found without difficulty. The two propositions which 
are given contain the three terms of the syllogism ; one 
of these will be common to the two propositions, and the 
missing proposition will contain the other two terms. 
Thus with the proposition, " S is M ; hence, S is P," 
the missing premise is clearly " M is P," or " P is M." 
With " M is P ; therefore, S is P," the missing premise 
will contain S and M. 

The danger of false reasoning is greater here than 
in the complete syllogism, since the proposition which 
is not expressed may be false or inadequate, and if the 

151 



152 HYPOTHETICAL SYLLOGISMS 

proposition is not definitely stated its inadequacy is 
easily overlooked. 

The Enthymeme is an incomplete form of syllogistic 
reasoning ; it is less than a syllogism. There are several 
complex forms in which we find more than a syllogism. 

Prosyllogism and Episyllogism. — Two complete 
syllogisms may be united by having a proposition in 
common. Thus : 

{All the Romance languages are derived from 
Latin; 
rrencii is a Romance language; 
Therefore_, French is derived from Latin. 
. . I This man speaks French; 

Episyllogism J Therefore, this man speaks a language de- 

[ rived from Latin. 

In this example the conclusion of the first syllogism 
is the major premise of the second. This is known as 
Prosyllogism and Episyllogism, the conclusion of the 
Prosyllogism being the major premise of the Episyllo- 
gism. One syllogism might, of course, establish the 
minor premise of the other: 



Prosyllogism 



French is a Romance language; 
This man speaks French. 
Therefore, this man speaks a Romance lan- 
guage. 

fAll the Romance languages are derived from 
Episyllogism J Latin; 

Hence, tins man speaks a language derived 
from Latin. 

Again, it might have each of its premises established 
by another syllogism: 



PROSYLLOGISM AND EPISYLLOGISM 153 



r 



Prosyllogism ^ 



Prosyllogism < 



Everything which is able to restrain trade 

is a source of danger; 
Every monopoly is able to restrain trade; 
Hence^ every monopoly is a source of 

danger. 

r- 

A company which has complete control of 

a certain commodity is a monopoly; 
This trust has complete control of a cer- 
tain commodity; 
Hence^ this trust is a monopoly. 
Conclusion: Therefore^ this trust is a 
source of danger. 



An enthymeme might take the place of the complete 
syllogism in the case of either or both of the prosyllo- 
gisms. Further, the premises of the prosyllogisms 
might themselves be supported by other syllogisms. 

A great many syllogisms may be combined into one 
reasoning process, and most reasoning processes con- 
tain several syllogisms, complete or abbreviated.^ 



1 Geometrical reasoning illustrates abbreviated reasoning very 
clearly. For example take the proof of the proposition that " All 
straight angles are equal." 



A "^ B 

D E p 



"Let the angles ACB and DEF be any two straight angles. 
To prove that the angle ACB equals the angle DEF. 

" Place the angle ACB on the angle DEF, so that the vertex C 
shall fall on the vertex E, and the side CB on the side EF. Then 
CA will fall on ED. Therefore the angle ACB equals the angle 
DEF." (Wentworth, Plane Geometry, page 14.) 

This is the proof in an abbreviated form. It might be more 
fully expressed as follows; {See 'page 134.) 



154 



HYPOTHETICAL SYLLOGISMS 



We might have a chain of syllogisms in which the 
conclusion of each was the minor premise of the one 
following. 

All ungulates are mammals. 
All mammals are warm-blooded. 
All ungulates are warm-blooded. 

All warm-blooded animals have lungs. 
All ungulates are warm-blooded animals. 
All ungulates have lungs. 

All animals that have lungs require air. 
All ungulates have lungs. 
All ungulates require air. 



What is true of the angles ACB and DEF will be true of all 
straight angles. 

Two angles which can be so placed upon each other that 
their vertices coincide and their sides coincide are 
equal, each with the other. 

Any figure may be moved from one place to another 
without altering its shape. (Axiom of superposi- 
tion.) Therefore, the figure ACB may be placed 
upon the figure DEF without altering its shape. 
( Straight angles are such as have their sides ex- 
tending in opposite directions so as to be in 
the same straight line. The angles ACB and 
DEF have their sides so extending. Hence 
the lines AB and EF are straight lines. 

Two straight lines which have two 
points in common coincide and 
and form but one line. 
When the figure ACB is super- 
posed on the figure DEF so that 
the vertex C shall fall on the ver- 
tex E, and the side CB on the 
side EF, the straight line AB 
falls on the straight line DF and 
they coincide; the line CA falls 
on the line ED, and coincides 
with it, CB coincides with EF, 
[And C coincides with E]. 
1^ Therefore the angle ACB and the angle DEF are equal. 
Therefore all straight angles are equal. 
Geometrical reasoning is not all syllogistic in the narrowest 
sense of the word. See chapter xvii. 



THE SORITES 155 

The Sorites. — Now, instead of putting the conclu- 
sion in words and repeating it in the succeeding propo- 
sition, we may omit everything except the new premises 
until we are ready to draw the final conclusion. Thus : 

All ungulates are mammals. A is B 

All mammals are warm-blooded. B is C 

All warm-blooded animals have lungs. C is D 

All animals that have lungs require air. D is E 

Hence^ All ungulates require air. A is E. 

This is known as the Sorites; a Sorites may have any 
number of members. There are two forms. That given 
above, is an example of the Progressive or Aristotelian 
Sorites. The premise containing the subject of the 
conclusion (the Final Minor) comes first in order; that 
containing its predicate (The Prime Major) comes 
last; the intermediate propositions serve to connect the 
two. In the Regressive or Goclenian Sorites, the Prime 
Major comes first and the Final Minor last among the 
premises. If expanded into a chain of prosyllogisms 
and episyllogisms, the conclusion of each syllogism 
would be. the major premise of the one following. For 
example : 

A European is a Caucasian. B is A 

A Frenchman is a European. C is B 

A Parisian is a Frenchman. D is C 

This author is a Parisian. E is D 

Hence^ This author is a Caucasian. E is A 

In both forms of the sorites the reasoning is in the 
first figure of the syllogism. With the exception of 
the terms which are contained in the conclusion, every 
term in the sorites is a middle term. The greatest 
source of danger in this form of reasoning is to be 
found in ambiguous terms. 



156 HYPOTHETICAL SYLLOGISMS 

Only the Final Minor premise may be particular; 
only the Prime Major may be negative. 

Hypothetical Reasoning. — The forms of reasoning 
with which we have been dealing in the last three chap- 
ters have employed only declarative sentences, or Cate- 
gorical Propositions, as they are called in Logic. A 
categorical proposition is an unconditional statement. 
" A is B " or " A is not B '' are typical forms. But 
there are other kinds of propositions ; one of these is 
the Hypothetical Proposition, A hypothetical prop- 
osition is one containing a categorical proposition and 
th^ statement of a condition on which the truth of the 
categorical depends. The conditional member of the 
proposition is called the Antecedent; the categorical 
member is called the Consequent, A hypothetical propo- 
sition may be made the major premise of a syllogism. 

Such a syllogism would be a Hypothetical Syllo- 
gism. The Hypothetical syllogism has four forms. 

1. If A is B_, C is Dc If the substance is carbon^ it will 

burn. 
A is B It is carbon. 

.*. C is D /.It will burn. 

2. If A is B^ C is D. If the substance is carbon, it will 

burn. 
A is not B It is not carbon. 

.*. C is not D .'.It will not burn. 

3. If A is B, C is D. If the substance is carbon, it will 

burn. 
C is D It will burn. 

.*. A is B /.It is carbon. 

4. If A is B, C is D. If the substance is carbon, it will 

burn. 
C is not D It will not burn. 

/.A is not B /.It is not carbon. 



^^E HYPOTHETICAL SYI.LDGISM 157 

The first of these affirms the antecedent, the second 
denies it ; the third affirms the consequent, and the 
fourth denies it. The second and third are obviously 
invahd. The fact that the substance is not carbon 
gives us no further information about quahties ; and the 
fact that it will burn does not insure its being carbon. 
These instances are typical and illustrate the general 
rule that Denying the antecedent or affirming the conse- 
quent in a hypothetical syllogism are invalid forms of 
reasoning?' 

We may have a hypothetical syllogism in which the 
minor premise is also a hypothetical proposition. 

If A is B, C is D. If he is nominated^ he will be 

elected. 

If C is D^ E is F. If he is elected^ this measure 

will not pass. 
.'.If A is B^ E is F. /.If he is nominated^ this meas- 
ure will not pass. 

Disjunctive Reasoning. — There is a third kind of 
so-called syllogism with still another sort of proposi- 
tion as its major premise. This is the Disjunctive 
Syllogism and its major premise is a Disjunctive Prop- 
osition. A disjunctive proposition is one which states 
an alternative. " A is either B or C " ; " It will either 
rain or snow." The minor premise either affirms or 

2 There are cases, however, in which these forms give true 
conclusions. If the antecedent is the only one on which the con- 
sequent would follow then all the forms of the hypothetical syllo- 
gism would give valid conclusions. For example, if we had the 
major premise, "If A is B, and in no other case, C will be D," 
then to deny that A is B would necessitate the conclusion that C 
is not D. We may take, as a concrete case, " If a triangle is 
equilateral, and in no other circumstances, it will be equiangular. 
This triangle is not equiangular ; hence it is not equilateral " ; or, 
" This triangle is equilateral, therefore it is equiangular," and 
so on. 



1S8 HYPOTHETICAL SYLLOGISMS 

denies one of the alternatives. The conclusion either 
denies or afBrms the other. 

A is either B or C It will either rain or snow* 

A is B It will rain. 

/.A is not C /.It will not snow. 

A is either B or C It will either rain or snow. 

A is C It will snow. 

/.A is not B .Mt will not rain. 

A is either B or C It will either rain or snow. 

A is not B It will not rain. 

.'.A is C .'.It will snow. 

A is either B or C It will either rain or snow. 

A is not C It will not snow. 

.'.A is B .'.It will rain. 

All these forms are valid. The only source of danger 
is in the major premise. If the alternatives are not 
true alternatives, the conclusion can not be trusted. If 
A can be anything else than B or C, or if it can be both 
at the same time, the denial or affirmation of one alter- 
native cannot assure us of the truth or falsity of the 
others. 

There are more complex forms of disjunctive reason- 
ing ; we might, for example, have the proposition, "' A 
is B or C or D, etc." In this case the affirmation of one 
would mean the denial of the other two ; but the de- 
nial of one would give as the conclusion a disjunctive 
proposition containing the two others as alternatives. 
Thus " A is not B ; A is either C or D, etc." Similarly 
the assertion " A is B or C " would give the conclusion 

A is not D, etc.," and so on. 



ii 



THE DILEMMA 159 

There are certain imperfect forms of this syllogism 
which are sometimes useful. Sometimes we know that 
A is B or C or, it may be, both. In such a case, if we 
know that A is not B, then it must be C, but if we know 
that it is B, we do not know that it is not also C. With 
such a major premise, the minor premises which are 
affirmative do not give valid conclusions. It would be 
simpler in such cases to state the three possibilities as 
mutually exclusive, " A is B or C, or both B and C," and 
proceed as in the perfect forms of the hypothetical 
syllogism. 

More Complex Forms. The Dilemma. — There are 
more complex forms of reasoning in which hypothetical 
and disjunctive propositions are combined. Thus we 
may have: 

If A is B, C is D or E (or C is D or E is F). 
A is B. .'. C is D or E {or C is D or E is F). 

More concretely : 

If he fails^ he will leave college or drop back a class. 
But he is sure to fail. 
.'. He will leave college or drop back a class. 

If the antecedent were denied there could be no valid 
conclusion ; in this and all other respects this syllogism 
is like a simple hypothetical syllogism except in having 
a disjunctive consequent, instead of a categorical one. 
We get more complicated forms when the major pre- 
mise consists of two hypothetical propositions, in which 
either the antecedents or the consequents are found to 



160 HYPOTHETICAL SYLLOGISMS 

be alternative: the minor premise Is a disjunctive 
proposition, and the resulting syllogism Is a Di- 
lemma. 

If A is B, C is D; and if E is F, C is D. 
But either A is B or E is F. 
.*. C is D. 

If a college education gives a student useful information, 
it is valuabl|^ to him. 

If it gives him mental training it is valuable to him. 

But it either gives him useful information or mental 
training. 

/.It is valuable to him. 

This is a Simple Constructive Dilemma: simple be- 
cause the consequents of the hypothetical propositions 
in the major premise are the same in both cases; con- 
structive because it establishes an affirmative conclu- 
sion. 

If the consequents were denied we should not have a 
dilemma, but two simple hypothetical syllogisms. There 
would be no disjunctive premise. 

The second form of the dilemma Is the Complex Con- 
structive Dilemma. In this, the consequents of the 
hypothetical propositions In the major premise are not 
the same. 

If A is B, C is D; and if E is F, G is H. 
But either A is B or E is F. 
.'. Either C is D, or G is H. 

" If a statesman who sees his former opinions to be 
wrong does not alter his course he is guilty of deceit; and 
if he does alter his course he is open to a charge of incon- 
sistency; but either he does not alter his course or he does; 
therefore, he is either guilty of deceit, or he is open to a 
charge of inconsistency." (Jevons, Lessons in Logic, p. 
168.) 



THE DILEMMA 161 

Unlike the simple dilemma, this has a disjunctive 
conclusion. 

The Complex Destructive Dilemma has a negative 
minor premise and a negative conclusion. 

If A is B, C is D ; and if E is F, G is H. 
But either C is not D or G is not H. 

/. Either A is not B or E is not F. 

lb 

" If this man were wise^ he would not speak irreverently 
of the Scripture in jest; and if he were good he would not 
do so in earnest; but he does it either in jest or in earnest; 
therefore^ he is either not wise^ or not good. (Whately, 
Elements of Logic,) 

If the minor premise were " Neither C is D nor G is 
H " we should not have a dilemma. The minor premise 
would not be disjunctive and we should have two simple 
hypothetical syllogisms. 

Asserting that one or the other of the antecedents 
was false, or that one or the other of the consequents 
was true would be fallacious, as in the case of the simple 
hypothetical syllogism. 

In practice it is very difficult to find true major 
premises for a dilemma. Moreover, " a dilemma can 
often be retorted by producing as cogent a dilemma to 
a contrary eflFect. Thus an Athenian mother, accord- 
ing to Aristotle, addressed her son in the following 
words : " Do not enter into public business ; for if you 
say what is just, men will hate you; and if you say 
what is unjust, the gods will hate you." To which 
Aristotle suggests the following retort : " I ought to 
enter into public affairs; for if I say what is just, the 
gods will love me; and if I say what is unjust, men 
will love me." (Jevons,) 



162 HYPOTHETICAL SYLLOGISMS 

The conclusion of a dilemma, as of any other form 
of reasoning, may serve as a premise for further rea- 
soning. 

Extra-syllogistic Reasoning. — Certain other forms 
of reasoning call for some discussion here. They are 
not syllogistic, but they are closely related to syllo- 
gistic reasoning. For example, " A is taller than B ; 
B is taller than C ; therefore A is taller than C." This 
is not a syllogism. There are five terms in the reason- 
ing; A, B, C, taller than B, and taller than C. There 
is a similar difficulty in this : " M is east of N ; N is 
east of O, therefore M is east of O." It would, of 
course, be possible to construct a syllogism which would 
cover the ground in each of these cases. Thus, " What- 
ever is taller than another thing is taller than every- 
thing which is shorter than that thing; A, B, and C 
present a case, etc." And similarly in the other example. 
Some such principles as these are implied, but the rea- 
soning as stated is not in the form of a simple syllo- 
gism. We have here a system of relations which is more 
complicated than that found in the ordinary syllogism. 
In the latter we need have only our premises and the 
ordinary laws of reasoning, to assure our conclusion ; 
in reasoning of the sort illustrated in these examples 
we must have, besides our premises, a supply of in- 
formation about the general system of things to which 
the data in question belong. When such reasoning is 
thrown into the syllogistic form the major premise 
states the main principles of the system, as in the ex- 
ample above. Sometimes our information about the sys- 
tem would be sufficient to warrant a conclusion and 
sometimes it would not ; sometimes the fact that two 



EXTRA-SYLLOGISTIC REASONING 163 

things are related to a third gives us information re- 
garding their relations to each other and sometimes it 
does not. From the statements that " A is the employer 
or friend or enemy of B " and that " B is the em- 
ployer or friend or enemy of C," we could not draw 
any conclusion with regard to A's direct relations to 
C. Things equal to the same thing are equal to each 
other, but it is not necessarily true that things unequal 
to the same thing will be unequal to each other. In 
the latter case there are two possibilities ; the system 
is not clearly enough defined to make certain any con- 
clusion at all. This was true in some of the illustra- 
tions given above. To decide in any given case we must 
first determine whether the set of relations involved is 
completely enough known to justify a conclusion; in 
other words, Is more than one conclusion possible? 
Sometimes the system may be very complex, but its parts 
may be so related to each other and so completely 
known as to make a conclusion possible. A conclusion 
may simply state the relation of the terms in a reverse 
order. " A is east of B, therefore B is west of A." The 
conclusion may represent a pathway through a system 
from one particular part to another ; while the premise 
may be merely the same pathway followed from the 
other end. If A is the son-in-law of the half-sister of 
B's grandfather, then B is the grandson of the half- 
brother of A's mother-in-law. The system might have 
any degree of complication whatever, but if the several 
relations could be read from either end the pathway 
could be followed in either direction. Reasoning of 
this sort might be regarded as a broader form of con- 
version.^ 

3 See Aikins, Principles of Logic, chap. xi. 



164* HYPOTHETICAL SYLLOGISMS 



EXERCISES. 

1. Supply the missing proposition's in the following: 

(1) He is a politician and therefore not to be 

trusted. 

(2) They were all brave men and this man was one 

of them. 

(3) Whales have warm blood but fish do not. 

(4) Only members will be admitted; that excludes 

you. 

2. Determine which of the following give valid conclu- 
sions and which do not; point out the fallacies involved: 

(1) If he goes^ I shall remain; but he will not go. 

(2) If he goes^ I shall remain; and I shall remain. 

main. 

(3) I shall remain if he goes; and he will go. 

(4) If it rains to-morrow^ the game will be post- 

poned; the game will be postponed. 

(5) If all the sides of this triangle are equal its 

angles are equal too; now its angles are not 
equal. 

(6) If he fails it will be because he has not worked 

hard; and he has not worked hard. 

3. Criticise the following^ stating the form of reasoning 
in each case: 

(1) A great man must either have extraordinary 

natural ability or exceptional capacity for 
work; this man had extraordinary natural 
ability^ hence we may assume that his capacity 
or work was not unusual. 

(2) If the government enacts such a law it must 

either adopt socialism or go into bankruptcy; 
but it will not enact such a law; so there is no 
danger of either socialism or bankruptcy. — 
L^ (Hyslop.) 

(3) If capital punishment involves cruelty to its 

victims it ought to be abolished in favor of 

some other penalty; if it does no good for so- 

Vx ciety it should also be abolished. But either 

> ' it involves cruelty to its victims or it does no 



EXERCISES 165 

good to society^ and hence it ought to be abol- 
ished. — (Hyslop.) 

(4) If he sinks he will be drowned^ and if he swims 

he will be captured by the enemy ; but he must 
^— ^ either sink or swim; therefore^ he will either 

be drowned or captured by the enemy. 

(5) If he tells the truth he will be forgiven^ and 

if he does not he will escape detection; but 
,^vjj' either he will be forgiven or he will escape 
detection ; hence he will either tell the truth 
or he will not. 

(6) If he did that intentionally he is not wise^ and 

if he did it unintentionally he is not lucky; 
but he is neither wise nor lucky; therefore^ he 
did it neither intentionally nor unintention- 
ally. 
4. In a sorites why must all the premises except the 

prime major be affirmative and all except the final minor 

be universal.^ 



iVv ^ *^ Vv V ^- 



L 



CHAPTER XI 

I. PROOF AND DISPROOF. II. FAILURE TO 

PROVE 

I. Various Kinds of Proof. — The conclusion of a 
valid syllogism is proved; and so also is the conclusion 
of each of the other forms of reasoning which we have 
examined. A proposition is proved when it is shown 
to be the necessary consequence of any combination of 
admitted propositions. All the cases which we have so 
far examined are instances of direct proof. In direct 
proof we show that, granted certain things, the con- 
clusion necessarily follows. A conclusion is proved only 
when it is shown that the conclusion must be true. 

There are several other kinds of proof ; in this chap- 
ter we shall consider the other kinds, and also the va- 
rious forms of failure to prove, or fallacy. 

Indirect Proof. — The first to be considered is 
indirect proof ; we prove a proposition indirectly by dis- 
proving its contradictory, i, e,^ by showing that its con- 
tradictory cannot be true. 

To disprove a proposition it is necessary to find some 
admitted fact or truth which is inconsistent with it. 
For instance, if we can show that the contrary or con- 
tradictory of a proposition is true, the proposition 
must be false. More concretely, if we have an A propo- 
sition, the contradictory would be an O proposition ; if 
we can show that O is true, A is necessarily false, and 
to show the truth of O we need find only one real ex- 

166 



INDIRECT PROOF 167 

ception to A. Showing the truth of E would also dis- 
prove A; but E is a universal proposition, and it is 
obviously much more difficult, in ordinary circum- 
^ stances, to prove a universal than it is to prove a par- 
ticular. Similarly the truth of I or of A would mean 
the falsity of E, etc. 

In indirect proof, we disprove the contradictory, not 
the contrary, for the falsity of the contrary does not 
prove the truth of the proposition, since both contraries 
may be false ; but if the contradictory is false, the prop- 
osition must be true, for one of two contradictories 
must be true. Suppose then that we wish to prove 
an A proposition : if we can show, in any way, that the 
corresponding O proposition would be false or absurd 
— contrary to fact or reason — our thesis is proved. 

The contradictory is usually disproved by show- 
ing that some of its necessary consequences are ab- 
surd. 

Indirect proof is frequently employed in geometry 
and it is there that the best examples of it are to be 
found. It is also a frequent resource in political de- 
bate, but in that field the facts are so complicated and 
the matter of establishing any proposition so liable to 
error that the grounds of any conclusion established 
in this way must be very carefully examined. 

We shall consider briefly two other special forms of 
proof, which are perhaps reducible to direct proof, but 
they are apparently very different from what we find 
in the syllogism and they will therefore be considered 
separately. The first is found in geometrical reasoning. 

Proof in Geometry. — In geometrical proof we seem 



168 PROOF AND DISPROOF 

to be founding a universal conclusion upon a single 
case; how is it possible for us to have perfect confidence 
in a conclusion which seems at first sight to be an in- 
duction from one isolated figure? If the individual 
peculiarities of the figure had anything to do with sup- 
porting the conclusion the latter would of course be 
of very slight value ; we should have no assurance that 
the next example might not be inconsistent with the 
conclusion. The certainty of the conclusion rests upon 
the fact that the figure used in the demonstration is, in 
all essential respects, like every other figure to which 
the proof is supposed to apply. The figure employed 
is purely symbolical; it stands for certain universal re- 
lations. If the truth of the conclusion follows from 
the characteristics which the present figure has in com- 
mon with all others of the class, then it will be true for 
all such figures, and the peculiar characteristics will 
have nothing to do with the case. The major premise 
underlying demonstration by means of figures is this: 
'' The present figure is an adequate representative of 
all figures to which the present proof applies." 

The second special form of proof which we shall 
examine is found in what is known as mathematical in- 
duction. 

Proof by Mathematical Induction. — The follow- 
ing illustration is a typical example of reasoning of the 
sort just mentioned. " If we take the first two consecu- 
tive odd numbers, 1 and 3, and add them together the 
sum is 4, or exactly twice two; if we take three such 
numbers, 1 -f 3 + 5, the sum is 9, or exactly three times 
three; if we take four, namely 1 + 3 4- 5 + 7, the sum is 



MATHEMATICAL INDUCTION 169 

16, or exactly four times four; or generally, if we take 
any number of the series, I + S + S' + Th-...., the sum 
is equal to the number of terms multiplied by itself. 
Any one who knows a little algebra can prove that this 
remarkable law is universally true, as follows : Let n be 
the number of terms, and assume for the moment that 
this law is true up to n terms, thus : 

• 1+3+5+7+ +( 2/1-1 )=7^^ 

Now add 9.n + 1 to each side of the equation. It fol- 
lows that: 

l + 3 + 5 + t+ + (2/^ - 1) + (2/1 + 1) =7i2 + 2/1 + 1 

But the last quantity, /i^ + 2/1 + 1, is just equal to 
(/I + 1)^ ; so that if the law is true for n terms it is true 
also for /i + 1 terms. We are enabled to argue from 
each single case of the law to the next case ; but we 
have already shown that it is true of the first few cases, 
therefore it must be true of all." ^ If what is true of 
any case is true of the one following it, it will be true of 
all cases whatsoever- It sometimes happens that some- 
thing is true of a great many successive cases without 
being really general. To quote again from Jevons : 
" It was at one time believed that if any integral num- 
ber were multiplied by itself, added to itself, and then 
added to 41, the result would be a prime number, that 
is, a number which could not be divided by any other 
integral number except unity ; in symbols, ^^ + a? + 41 
= prime number. This was believed solely on the 
ground of trial and experience, and it certainly holds 
1 Jevons, Lessons in Logic, pp. 220-921. 



170 PROOF AND DISPROOF 

for a great many values of x. . , . No reason, how- 
ever, could be given why it should always be true. ... 
it fails when cc - 40."' " We can perceive no simi- 
larity between all prime numbers which assures that be- 
cause one is represented by a certain formula, also 
another is ; but we do find such similarity between the 
sums of odd numbers." 

Here, as elsewhere, if one or a few cases are adequate 
representatives of a whole class of cases, what is true 
of the present case or cases will be true of all, and a 
universal conclusion can be drawn from a single case. 
The great difficulty in ordinary inductions is to be sure 
that the given case is an adequate representative. Or- 
dinarily the facts are very complex and the inspection 
of a single case is not sufficient to show us the charac- 
teristics which an adequate representative of the class 
should possess. In other words, we do not know what 
circumstances are relevant. In selecting cases for the 
application of the several inductive methods, the selec- 
tion is for the purpose of enabling us to determine what 
circumstances are relevant. 

II. Failure to Prove: Fallacies. — Let us examine 
the various ways in which proof may be vitiated, the 
various fallacies to which reasoning is liable. Some 
of these have been discussed already, but they will be 
mentioned again here and the other fallacies not pre- 
viously noted will be examined. 

Fallacies of Language. — In the first place we may 
mistake the meaning of the premises owing to the fact 
that we have not understood the language in which they 
are expressed. The Fallacies of Amphiboly, Accent, 
Figure of Speech (see chapter v), are cases in point. 



FALLACIES 171 

Again, to mistake the general for the specific use of 
a term, or the concrete for the abstract, or to use a 
term in one sense in one part of the reasoning and in 
another sense in another part, would render the con- 
clusion unsound; the Fallacy of Accident must be 
guarded against. (See page 55,) 

Once more, we may mistake the collective for the dis- 
tributive use of a term or vice versa, or we may use a 
term in one of these senses in one part of the reasoning 
and in the other sense lin another part ; this would in- 
volve us in a Fallacy of Composition or of Division, 
(See page 57.) 

Fallacies of Assumption. — Again, if we use as a 
premise in our reasoning a proposition which is not 
established, such as an insufficiently verified inductive 
inference, our conclusion is not proved. It may be true, 
or it may not be, but a conclusion is not proved so long 
as there is a possibility that it may be false. When we 
use a proposition of this sort to support a conclusion 
we are said to commit the Fallacy of Begging the Ques- 
tion^ or, to use the scholastic term, Petitio Principii. It 
is frequent in cases in which one has a thesis to prove 
and he sees that a certain proposition will enable him to 
prove it (it may be either premise in a syllogism — or 
both). He therefore assumes the truth of this proposi- 
tion on insufficient grounds, sometimes on very slight 
grounds. 

To decline to admit a premise because we see that it 
necessitates an unwelcome conclusion is to commit this 
fallacy. 

A false categorical proposition, an incorrect hypo- 
thetical proposition, or a disjunctive proposition in 



172 PROOF AND DISPROOF 

which the disjunction is not complete, would also, if 
used as premises, be illustrations of this fallacy. It is 
not even necessary to use a complete proposition to 
commit this fallacy ; the use of a name or an epithet 
may lead to fallacious conclusions ; the name or epithet 
does, to be sure, imply a proposition. To argue that 
this criminal should be punished, because all criminals 
are a menace to society, begs the question if it has not 
been shown that this man is a criminal. The epithet is 
sometimes more dangerous than the implied proposition 
would be, for we are less likely to notice that something 
has been assumed when the Droposition is only sug- 
gested. 

One form of the Petitio Principii is Arguing in a 
Circle, or Circulus in Probando. In this, the premise is 
simply the desired conclusion stated in other words. To 
say that man is a conscious being because he has mental 
states, is to argue in a circle, since to be a conscious 
being is to have mental states. When the argument 
is short there is little to be feared from this fallacy ; 
the identity in meaning of the two statements is easily 
discovered if they come close together; but in a long 
argument the first may be only vaguely remembered by 
the time the second is made, and if the reasoning has 
not hitherto been questioned the fallacy may escape 
detection. A language like English, which is very rich 
in synonyms, offers very many occasions for this fal- 
lacy. 

Another closely related fallacy is that known as the 
Fallacy of Many Questions or sometimes Double Ques- 
tion. One of the traditional illustrations is, " Have 
you left off beating your wife.^ " Whichever answer is 



FALLACIES 173 

given. Yes or No, seems to admit the truth of the im- 
phcation. In this fallacy, the question assumes the 
truth of something which is not proved or admitted, and 
which may be false. It demands a direct answer, and 
no direct answer can be given without an apparent ad- 
mission of the thing assumed. 

Formal. Fallacies. — There are several fallacies 
which result from the violation of the principles of 
syllogistic reasoning. These are usually called the 
Formal Fallacies^ because they are said to result from 
violating the formal laws of the syllogism, the laws re- 
lating to the number of terms and the distribution of 
terms in the syllogism. We might include also, Fal- 
lacies of Illicit Conversion and Ohversion, Creighton 
includes them in Fallacies of Interpretation? Using 
four terms instead of three gives the Fallacy of Four 
Terms, Distributing the major term in the conclusion 
when it has not been distributed in the premise gives 
the Fallacy of Illicit Distribution of the Major Term, 
and distributing the minor term in the conclusion when 
it was not distributed in the premise gives the cor- 
responding Fallacy of the Minor Term, Failing to 
distribute the middle term gives the Fallacy of Undis- 
tributed Middle, There are also the Fallacies of Two 
Negative Premises, and Two Particular Premises. 

This is the way in which violations of the laws of 
syllogistic reasoning have usually been classified. As 
we have already seen, these violations can also be dealt 
with as failures to comply with the principles of the 
Four Figures. The latter method is less formal and 
more in accordance with our ordinary habits of thought, 

2 See his Logic, chapter xii. 



174 PROOF AND DISPROOF 

The Fallacies of Hypothetical Reasoning, Denying 
the Antecedent and Affirming the Consequent, belong 
in the class just discussed. 

The Conclusion May Not Follow From the 
Premises. — There is a form of false reasoning known 
as the Non Sequitur. In this the premises may be clear 
and true and there may be no fallacies of distribution 
or of negative premises, but the conclusion does not 
follow from the premises. It may be true enough and 
provable on other grounds but it does not belong to the 
propositions on which it has been based. It was origi- 
nally called the Fallacy of False Consequent and had to 
do with hypothetical reasoning, but the term Non 
Sequitur is now applied to categorical reasoning in 
which the conclusion does not follow from the premises. 
De Morgan's illustration (quoted by Hyslop) is as fol- 
lows : 

Episcopacy is of Scripture origin. 

The Church of England is the only Episcopal Church 
in England. 

Therefore, the church established is the church that 
should be supported. 

This fallacy, like the rest, is more likely to pass un- 
noticed in a long argument than in a short one. 

A similar fallacy, sometimes treated as a form of the 
last, is that of False Cause, or Non Causa pro Causa, 
or Post Hoc ergo Propter Hoc, This consists in argu- 
ing that because one thing has followed another, it is 
therefore the effect of that other, as if one should argue 
that because a panic followed the adoption of a certain 
measure, it was therefore caused by that measure. 

Missing the Point. — One more fallacy is to be 



FALLACIES 175 

noted; that in which the argument is not to the point. 
The reasoning may with entire correctness prove some- 
thing but it is not the thing which was to be proved. 
An opponent is sometimes charged with shifting the 
ground of debate ; that means usually that he is no 
longer trying to prove the thesis with Avhich he started 
but something else more or less closely related to it. 
This is known as the Fallacy of Ignoratio Elenchi. 
Several forms have been distinguished. One of these is 
the Ad Hominem argument ; in this, instead of being 
to the point, the argument is directed against the char- 
acter or consistency, etc., of the opponent or some 
other person. When an advocate proves the prisoner's 
good character and assumes that he has proved his in- 
nocence of the crime with which he is charged, he is 
guilty of this fallacy. When a debater attacks his op- 
ponent instead of proving his thesis he commits this 
fallacy. It is a method of silencing an opponent but 
not of proving a case. Appeals to authority, to pre- 
judice, to emotion, are all forms of the fallacy of 
Ignoratio Elenchi, as is also the argument in which the 
victory depends upon the fact that the opponent has 
not the information necessary to enable him to meet 
the argument. 

When we assume that a proposition is false because 
the arguments in its support have been discredited, we 
commit this fallacy. The proposition is only not 
proved, instead of being disproved. A good cause may 
suffer from bad arguments because of the widespread 
tendency to commit this fallacy. 

In most arguments many of the propositions involved 
are unexpressed. In such cases it is often difficult to 
know what fallacy to charge against reasoning which 



176 PROOF AND DISPROOF 

is obviously unsound. Suppose we have the argument, 
" A classical course is useless because it trains for no 
profession;" what fallacies might be charged? In the 
first place we might say that the fallacy was a Non 
Sequitur ; the conclusion does not follow from the 
grounds which have been stated. It might be replied 
that there was a further premise understood, namely, 
" Every college course which does not train for a pro- 
fession is useless." The fallacy of Non Sequitur would 
be disposed of, but it would now be possible to charge 
the fallacy of Begging the Question, in the premise 
which has been supplied. Or it might be that the pre- 
mise understood was " Most courses of study which do 
not train for a profession are useless." That might 
possibly be true, but even admitting it, the reasoning is 
not valid, because it violates the principles of syllogistic 
reasoning. 

In cases of doubt the only way of being certain that 
we have been fair to an absent opponent or have met 
all replies to our criticisms, is to follow some such pro- 
cedure as that just illustrated and show that if one 
criticism can be met another cannot, or that, if the con- 
clusion is to be established, such and such propositions 
must be shown to be true. 

These fallacies are usually discussed in connection 
with the syllogism, but they may occur in the more com- 
plicated forms of reasoning as well. As we have 
already seen, the syllogism is the typical form of de- 
ductive reasoning, but there is much reasoning that is 
extra-syllogistic: although this might perhaps be put 
into syllogistic form such an operation is unnecessary 
if the premises and the steps in the argument are clear. 



FALLACIES 177 

In more complicated trains of reasoning which involve 
induction as well as deduction we must make sure not 
only of the reasoning processes, and of the clear state- 
ment of the premises, but also of the soundness of the 
premises, and of the grounds on which they are based. 

EXERCISES ^^ "''^'^^^ 

In the following exercises^ supply missing premises^ state 
the Figure in which the argument f alls^ and criticise fully 
the reasonings noting the fallacies of every sort: "> 

1. Personal deformity is an affliction of nature; dis- 
grace is not an affliction of nature; personal deformity is 
not a disgrace. ,u 

2. All paper is useful^ and all that is useful is a source 
of comfort to man; therefore^ all paper is a source of com- 
fort to man. 

3. If Caesar were a tyrant^ he deserved to die; but he 
was not a tyrant^ and therefore did not deserve to die, 

4. Every one desires his own good; justice and temper- 
ance are everyone's good; hence^ every one desires justice 
and temperance. 

5. Some of the inhabitants of the earth are more civi- 
lized than others; no savages are more civilized than other 
races; therefore^ no savages are inhabitants of the earth. 

6. He must be a Mohammedan^ for all Mohammedans 
hold these opinions. 

7. He must be a Christian^ for only Christians hold these 

opinions. 

8. All valid syllogisms have three terms; this syllogism 
has three terms^ and is therefore valid. '- ^' 

9. None but despots possess absolute power; the Czar 
of Russia is a despot; therefore^ he possesses absolute 

power. 

10. The right should be enforced by law; the exercise of 
the suffrage is a rights and should therefore be enforced 

by law. 

11. Nothing is better than wisdom; dry bread is better 
than nothing; therefore, dry bread is better than wisdom. 

12. Every rule has exceptions; this is a rule and there- 



178 , PROOF AND DISPROOF 

fore has exceptions; therefore^ there are some rules that 
have no exceptions. 

13. For those who are bent on cultivating their minds 
by diligent study^, the incitement of academical honors is 
unnecessary; and it is ineffectual for the idle and such as 
are indifferent to mental improvement; therefore^ the in- 
citement of academical honors is either unnecessary or 
ineffectual. 

14. Suicide is not always to be condemned^ for it is but 
voluntary death^ and this has been gladly embraced by 
many of the greatest heroes of antiquity. 

15. Theft is a crime; theft was encouraged by the laws 
of Sparta; therefore^ the laws of Sparta encouraged crime. 

16. Nothing but the express train carries the mail^ and 
as the last train was an express^ it must have carried the 
mail. 

^ 17. Protective laws should be abolished^ for they are in- 
j U' ^ jurious if they produce scarcity and useless if they do not. 
/ 18. Whosoever intentionally kills another should suffer 

death; a soldier^ therefore who kills his enemy should suf- 
fer death. 

19. The people of the country are suffering from famine; 
and as A^ B;, and C are people of the country^ they are 
therefore suffering from famine.^ 

20. Each of the books in the library is large; hence the 
library is large. 

21. Hunger is a sign of health; therefore^ famine which 
causes hunger is a good thing. 

22. Arsenic will kill a man; hence^ this medicine will kill 
you as it contains arsenic. 

23. The coat^ hat and dress were each in good taste; 
therefore^ the costume as a whole was in good taste. 

24. You can always trust to the majority to do what is 
right in the long run; this man is a member of the ma- 
jority^ and therefore he can be trusted to do what is right 
in the long run. 

25. Eating opium degrades and brutalizes a man; hence 

3 Most of the examples from 1 to 19 were borrowed from Hys- 
lop's Elements of Logic. A good many of them belong to the 
common stock. 



EXERCISES 179 

DeQuincy and Coleridge were low and degraded crea- 
tures. 

26. It is wrong to take life of fellow creatures ; hence 
it is wrong to kill a mad dog. 

27. Human life will at some time disappear from the 
earthy for every man must die. 

28. America is a Christian country; hence^ every Ameri- 
can is a Christian. 

29. The members of the college are students^ teachers, 
and administrative officers. The members of the football 
team are members of the college, and hence are students^ 
teachers, and administrative officers. 

30. If it is admitted that men who are proficient in 
engraving are of great service to a community, it must bcv. 
true that the greater the degree of excellence possessed by 
the counterfeiter, the better for the government. 

31. You must allow that this measure will do untold 
good to the country — that the whole community will prosper 
and that our nation will take its place with the foremost. 
You say you grant all this and still you maintain^that it will 
ruin your particular section. Is not your secticm a part of 
the nation, and will it not be benefited as well as the rest 
of the country? 

32. The population of the United States increased 20% 
between 1890 and I9OO; hence, the population of Vermont 
must have increased at that rate during the same period. 

33. Slavery was harmful to the development of the 
whole country, and hence to the South. 

34. Policemen must arrest all persons who block the 
highways or interfere with traffic. The policeman at this 
crowded corner does this, and should therefore be arrested. 

35. Kant held that all the proofs for the existence of 
God were fallacious. He was therefore an atheist. 

36. At the time of the Galveston flood men worked six- 
teen hours a day; hence, to talk of an eight-hour day as a 
necessity for the working classes is absurd. 

37. The evidence of the creator is the thing created. 

38. Before you stands the vile wretch who has been 
accused of murder. ^ V 

39. Why has man one more rib than woman .^^ 



180 PROOF AND DISPROOF 

40. The candidate is very fond of children^ and so no 
doubt she would be a good kindergarten teacher. 

41. This man's arguments are worthless^ for he is no- 
toriously dishonest. 

42. In answer to the argument that women^ as intelli- 
gent human beings^ are entitled to all the privileges of 
citizenship^ I ask you: Are not women like our sainted 
mothers^ who never held a ballot in their hands^ good enough 
for us ? 

43. '' Woman as well as man should have a part in the 
world's political affairs; for government is nothing but 
national housekeeping." 

44. *' More coffee is consumed in the United States than 
anywhere else^ and America has become the strongest 
nation." 

45. My opponent presents a formidable array of sta- 
tistics to prove that the country is financially unfit for war ; 
to which I am proud to reply that the old flag has never yet 
touched the ground. 

46. Agassiz did not accept the theory of Evolution; 
hence I, who know very little of biology^ am not justified 
in accepting it. 

47. This man was a good football player^ and hence will 
be a good man to write up the present football situation. 

48. A vacuum is impossible^ for if there is nothing be- 
tween two bodies they must be in contact. 

49. The government should be in the hands of the Demo- 
cratic party^ for the country could not help prospering un- 
der the supervision of the followers of Jefferson. 

50. It is indeed an opinion strangely prevailing amongst 
men^ that houses^ mountains^ rivers^ and in a word all sen- 
sible objects^ have an existence^ natural or real^ distinct 
from their being perceived by the understanding. But 
with how great an assurance and acquiescence soever this 
principle be entertained in the world^ yet whoever shall find 
it in his heart to call it in question may^ if I mistake not^ 
perceive it to involve a manifest contradiction. For^ what 
are the fore-mentioned objects but the things we perceive 
by sense? and what do we perceive besides our own ideas 
or sensations? and is it not plainly repugnant that any one 
of these^ or any combination of them^ should exist unper- 



EXERCISES 181 

ceived? — ^Berkeley^ Principles of Human Knowledge, 
Sec. 4. 

51. If there were external bodies it is impossible we 
should ever come to know it; and if there were not we 
might have the very same reasons to think there were that 
we have now. Suppose — what no one can deny possible — 
an intelligence without the help of external bodies^ to be 
affected with the same train of sensation or ideas that you 
are^ imprinted in the same order and with like vividness 
in his mind. I ask whether that intelligence hath not all 
the reason to believe in the existence of corporeal sub- 
stances^ represented by his ideas and exciting them in his 
mind^ that you can possibly have for believing the same 
thing? — Berkeley, Principles of Human Knowledge, 
Sec. 20. 

52. In the business of gravitation or mutual attraction, 
because it appears in many instances, some are straightway 
for pronouncing it universal; and that it attract and be 
attracted by every other body is an essential quality inher- 
ent in all bodies whatsoever. Whereas, it is evident that 
the fixed stars have no such tendency towards each other; 
and so far is that gravitation from being essential to bodies 
that in some instances a quite contrary principle seems to 
show itself; as in the perpendicular growth of plants in 
the elasticity of the air. — Berkeley, Principles of Human 
Knowledge, Sec. 106. 

53, '' The family, the state, religion and morality are 
all in danger in this country on account of divorces, accord- 
ing to the speakers at an Episcopal meeting in New York 
on Sunday. But are things in so bad a way? " In Eng- 
land, " so * horrible ' were the revelations of angry discon- 
tent with the married state made by hundreds of the cor- 
respondents of a London paper, that it was compelled 
recently to bring a discussion of the marriage question to 
an abrupt end." 

54. In arguing against the Darwinian Hypothesis, 
Agassiz is said to have urged the following: *' If species 
do not exist, how can they vary ? " 

55, Vegetarianism is a healthy diet, for all vegetarians 
find it so. 

56, No educated, much less a scientific person, who is 



182 PROOF AND DISPROOF 

convinced of the immutable order of things^ can now- 
adays believe in miracles. — Buchner^ Force and Matter, 

57. Either the laws of nature govern^ or the eternal 
reason governs ; if both govern together they must be in 
continual conflict; the government of the latter would 
render that of the former unnecessary^ whilst the action of 
unalterable laws admits of no personal interference^ and 
can on that account scarcely be called governing. A main 
point in the proof that the laws of nature are those of 
reason is^ that by thought we are able to deduce other laws 
of nature from those known to us^ so that we find them in 
experience^ and if this does not happen_, we naturally con- 
clude that we have formed erroneous conclusions. — Buch- 
ner^ Force and Matter. 

bS, In all parts of knowledge^ rightly so termed^ things 
most general are most strong; thus it must be^ inasmuch 
as the certainty of our persuasion touching particulars de- 
pendeth altogether upon the credit of those generalities 
out of which they grow. — Hooker^ Ecclesiastical Polity, 
i, 12. 

59. A spirit independent of nature cannot exist; for 
never has an unprejudiced mind^ cultivated by science^ per- 
ceived its manifestations. . . . How is it possible that 
the unalterable order in which things move should ever be 
disturbed without producing an irremediable gap in the 
worlds without delivering us and everything up to an arbi- 
trary power^ without reducing all science and every earthly 
endeavor to a vain and childish effort.^ — Buchner^ Force 
and Matter, 

60. Order and progress are two incompatible elements. 
Progress is accompanied by disorder^ by anarchy. For 
what is progress if not precisely the overturning of a given 
social order so as to institute a new one? — Draghicesco, 
Le probleme de la conscience. 

61. Sunshine is necessary for plants; for vegetable or- 
ganisms can not increase in size, sending roots into the soil 
and stems into the air, without the light and heat of the 
great solar luminary. 

62. Nothing is so bad that it cannot be worse. 

63. *' The canals are not so maintained. They are fall- 
ing into decay and disuse. The old boats are rotting and 



EXERCISES 183 

few new boats are built. The business of thfe canals falls 
oif^ and the city of New York^ which thirty years ago had 
75 per cent, of the foreign trade of the country^ now has 
less than 50 per cent.*' 

64. '' Philosophy bakes no bread." Then why waste 
time upon it? 

65. Men have a right to vote. Then where is the justice 
of depriving criminals of this right ? 

66. Two and three are even and odd; two and three are 
five; hence five is even and odd. 

67. To inflict capital punishment is to violate one of the 
commandments in the Decalogue. 

68. " The French drink more wine than any other nation 
and in literature and art they occupy a foremost place." 

69. "... it deals with the question exactly when the 
monstrous tariff is to be tenderly revised by its friends. 
The answer is * Never.' The thing cannot be done in pros- 
perous times^ because it would disturb business. In a 
period of depression^ it is out of the question^ as we then 
have troubles enough without opening Pandora's box. When 
affairs are just betwixt and between^ neither very good nor 
very bad^ no sagacious Republican would think of meddling 
with the tariff. Therefore^ we say the exact position of the 
Republicans is^ that an unj ust tariff is crying out for urgent 
revision^ that they are the only ones who can do the work, 
and that they will do it just one day after never." 

70. " The justice complains bitterly that the court has 
been obliged to resort to subterfuges in order to employ 
competent process-servers^ the eligible lists providing only 
worn-out soldiers who lack the essentials of youth^ deter- 
mination^ agility and vigor. He is therefore in favor of 
going back to the discredited system of * pass examina- 
tions ' or of re-enacting the starchless civil service law." 

71. In the domain of physics^ to the exploration of 
which Lord Kelvin has devoted an honored lifetime^ he 
would be a bold man who would cross swords with him. 
But for dogmatic utterance on biological questions there is 
no reason to suppose that he is better equipped than any 
person of average intelligence ... in the latter (organic 
nature) scientific thought is * compelled to accept the idea 
of creative power.' That transcends the possibilities of 



184 PROOF AND DISPROOF 

scientific investigation . . . Lord Kelvin^ in effect^ wipes 
out by a stroke of the pen the whole position won for us 
by Darwin. And in so doings it can hardly be denied that 
his present position is inconsistent with the principle laid 
down in his British Association address at Edinburgh in 
1871. — Extracts from letters written to the London Times 
apropos of Lord Kelvin's assertion regarding the limits of 
science. (Reprinted in Science.) 

72. The fact is so improbable that extremely good 
evidence is needed to make us believe it; and this evidence 
is not good^ for how can you trust people who believe in 
such absurdities.'^ 

73. The axioms of mathematics and the fundamental 
moral principles are inborn ; for tiiey are accepted by every- 
body. Moreover no reasonable being can deny them when 
he understands what they mean. 

74. I may doubt everything except that I think. I 
think^ therefore I exist. 

75. A parliamentary government is sure to fail in the 
long run; a battle may be won by a poor general but never 
by a debating society. 

76. Can anything be more ludicrous than first to build 
all our certainty of the assistance of the Holy Ghost upon 
the certainty of tradition and then afterwards to make the 
certainty of tradition to rely upon the assistance of the 
Holy Ghost. — Tillotson^ Rules of Faith. 

77. If men are not likely to be influenced in the per- 
formance of a known duty by taking an oath to perform 
it^ the oaths commonly administered are superfluous; if 
they are likely to be so influenced^ every one should be 
made to take an oath to behave rightly throughout his life; 
but one or the other of these must be the case; therefore 
either the oaths commonly administered are superfluous 
or every man should be made to take an oath to behave 
rightly throughout his life.* 

78. Few treatises of science convey important truths^ 
without any intermixture of error^ in a perspicuous and in- 
teresting form; and therefore^ though a treatise would 
deserve much attention which should possess such excellence^ 

4 The exercises from 77 to 90 are from Whately's Elements of 
Logic, 



EXERCISES 185 

it is plain that few treatises of science do deserve much 
attention. 

79. No one who lives with another on terms of con- 
fidence is justified, on any pretense^ in killing him; Brutus 
lived on terms of confidence with Caesar; therefore^ he was 
not justified^ on the pretense he pleaded^ in killing him. 

80. He that destroys a man who usurps despotic power 
in a free country deserves well of his countrymen; Brutus 
destroyed Caesar^ who usurped despotic power in Rome; 
therefore^ he deserved well of the Romans. 

81. Nothing which is of less frequent occurrence than 
the falsity of testimony can be fairly established by testi- 
mony; any extraordinary and unusual fact is a thing of 
less frequent occurrence than the falsity of testimony (that 
being very common) ; therefore^ no extraordinary and un- 
usual fact can be fairly established by testimony. 

82. Testimony is a kind of evidence which is very likely 
to be false; the evidence on which most men believe that 
there are pyramids in Egypt is testimony; therefore^ the 
evidence on which most men believe that there are pyramids 
in Egypt is very likely to be false. 

83. He who cannot possibly act otherwise than he does^ 
has neither merit nor demerit in his action; a liberal and 
benevolent man cannot possibly act otherwise than he does 
in relieving the poor; therefore, such a man has neither 
merit nor demerit in his action. 

84. The religion of the ancient Greeks and Romans was 
extravagant fables and groundless superstitions, credited 
by the vulgar and weak, and maintained by the more en- 
lightened, from selfish or political views; the same was 
clearly the case with the religion of the Egyptians; the 
same may be said of the Brahminical worship of India, and 
the religion of Fo, professed by the Chinese; the same, of 
the mythological systems of the Peruvians, of the stern and 
bloody rites of the Mexicans, and those of the Britons and 
Saxons ; hence we may conclude that all systems of religion, 
however varied in circumstances* agree in being super- 
stitions kept up among the vulgar, from interested or 
political views of the more enlightened classes. 

85. What happens every day is not improbable; some 
things against which the chances are many thousands to 



186 PROOF AND DISPROOF 

one^ happen every day; therefore^ some things against 
which the chances are many thousands to one are not im- 
probable. 

86. The principles of justice are variable; the appoint- 
ments of nature are invariable; therefore^ the principles of 
justice are not appointments of nature. 

87. Of two evils^ the less is to be preferred; occasional 
turbulence^ therefore^ being a less evil than rigid despotism_, 
is to be preferred to it. 

88. No evil should be allowed that good may come of it; 
all punishment is an evil; therefore^ no punishment should 
be allowed that good may come of it. 

89' Repentance is a good thing; wicked men abound in 
repentance; therefore, wicked men abound in what is good. 

90. If the exhibition of criminals, publicly executed, 
tends to heighten in others the dread of undergoing the 
same fate, it may be expected that those soldiers who have 
seen the most service, should have the most dread of death 
in battle; but the reverse of this is the case; therefore, the 
former is not to be believed. 

91. Why does a ball, when dropped from the masthead 
of a ship in full sail, fall not exactly at the foot of the 
mast but nearer the stern of the vessel? — Davis, Logic. 

92. ** The impious, whoever he may be, ought not to go 
unpunished. For do not men regard Zeus as the best and 
most righteous of the gods.^ And even they admit that he 
bound his father because he wickedly devoured his sons." — 
Plato, Euthyphro. 

93. The soul is unchangeable; the unchangeable is 
simple; the simple is indissoluble; the indissoluble is in- 
destructible; therefore, the soul is immortal. See Plato, 
Phaedo. 



PART II 
SUPPLEMENTARY METHODS 



^ 



CHAPTER I. 

STATISTICS 

The value of any conclusion depends largely upon 
the soundness of the premises from which it is drawn ; 
a great many of these premises, as we have seen, are 
inductions from particular facts. When these inductive 
inferences have been tested by one or another of the 
" Inductive Methods " they can be regarded as trust- 
worthy ; but the successful application of the methods 
presupposes a fairly complete analysis of the phe- 
nomena under investigation, for it is by this analysis 
that we determine the circumstances in which the 
phenomenon occurs. If we cannot determine the cir- 
cumstances it is obvious that we cannot apply the 
Methods. It might seem to follow from this that if 
the circumstances in which a phenomenon occurs are so 
complex as to defy analysis, or if the phenomenon itself 
cannot be separated into its elements, it would be im- 
possible to make any reliable generalizations regarding 
the relations of the phenomenon in question. Or if we 
were quite unable to surmise which of a multitude of 
circumstances was significant, or to isolate any of them 
by means of the Methods, we could not decide which was 
causally related to the phenomenon and which was not. 
There are many fields in which analysis is possible in 
only a slight degree ; social phenomena and phenomena 
of the weather are cases in point. A moment's reflec- 

189 



190 STATISTICS 

tion will show the difficulty of applying the Method of 
Agreement, for instance, in the study of the weather, 
or of the death rate. The phenomena are so exceed- 
ingly complex that anything approaching a complete 
statement of their elements is quite out of the question. 
The fallibility of most popular generalizations in these 
fields is evidence of the difficulty of dealing with such 
facts. Must we be content then simply to guess at the 
relations of such phenomena, with the slight assistance 
which is to be gained from so precarious a method as 
that of Simple Enumeration? In instances of this sort 
another method, a method which is closely related to 
the method of Simple Enumeration, becomes important : 
it is the Method of Statistics. In statistics we have an 
exact enumeration of cases. If a small number of cases 
does not enable us to detect the causal relations of a 
phenomenon, it sometimes happens that a large number, 
accurately counted, and taken from a field widely ex- 
tended in time and space, will lead to a solution of the 
problem. 

But how can the counting of cases aid in the discov- 
ery of a causal relation? It does so by showing the 
relative frequency of the phenomenon, its frequency as 
compared with some particular circumstance or circum- 
stances. If we noted only the phenomenon itself, knowl- 
edge of its frequency would be of little use. But if, in 
a large number of cases, taken from a wide field, we 
can find some other phenomenon correlated with the one 
we are investigating, then we have ground for a con- 
clusion. We proceed upon the principle that if the con- 
currence of two phenomena is merely a coincidence, the 



THE MEANING OF CORRELATION 191 

frequency of one should make no difference in the oc- 
currence of the other, and conversely that if there is a 
correlation^ there must he some causal relation. If the 
frequency of two phenomena is the same, or if varia- 
tions in the frequency of one correspond to variations 
in the frequency of the other, or if any change in the 
quantity or quality of one corresponds to changes in 
the frequency of the other, we are usually justified in 
inferring that something more than a coincidence is 
present. 

Correlation may be either positive or negative; in 
positive correlation the presence of a phenomenon A 
would mean the presence of the phenomenon B in a 
certain proportion of cases or in a certain amount, and 
so on; in negative correlation the presence of A would 
of course mean the absence of B in a certain propor- 
tion of cases, and so on. The relation between illiteracy 
and crime would be an instance of the former and the 
relation between vaccination and smallpox would illus- 
trate the latter. The total absence of correlation might 
perhaps be represented by the relation between the 
weather and the day of the month. Correlation can bq 
measured mathematically ; that is to say, it is possible 
to determine just what degree of correlation there is 
between two phenomena. The number which expresses 
this is called the coefficient of correlation. Complete 
positive correlation would be expressed by -1- 100, com- 
plete negative correlation by - 100, and absence of 
correlation by ; A coefficient of + 63 betw^een two 
phenomena would mean that one was present in 63 per 
cent, of the cases in which the other was present, or that 



192 STATISTICS 

the amount, or amount of increase, and so on, of one, 
was 63 per cent, of that of the other. ^ 

Sometimes ^ a correlation would not prove a direct 
causal relation ; the fact that the mortality among men 
is higher than that among women and bears a certain 
numerical relation to it, or the fact that about 106 
boys are born for every 100 girls, are examples of this. 
But there is nothing peculiar to statistics in this. The 
same thing appeared in connection with the method of 
Agreement; here, as there, the concurrence of two phe- 
nomena may mean that both are connected with some 
one underlying set of complex or undiscovered con- 
ditions. And even frequent concurrence may be acci- 
dental, though a thoroughgoing investigation would 
eliminate one which was entirely accidental. 

And even if the cause of a phenomenon Is not dis- 
covered in this way, it may be that its frequency 
is a matter of interest or of practical importance ; for 
its frequency may itself be a factor in determining our 
conduct ; the number of passengers stopping at a given 
railway station or the comparative number of boys and 
girls in a city may be worth knowing, even if not 
understood. The census reports contain a multitude of 
facts of this kind ; eventually the causal relations of 
many of them may be discovered. 

A statistical record like any other enables us to cor- 

1 For further discussion, see Thorndike, Mental and Social 
Measurements ; Bowley, Elements of Statistics; Pearson, The 
Chances of Death, 

2 It will be noted that the principles here employed are related 
to those used in the Methods of Agreement and of Concomitant 
Variations, but here analysis may be very incomplete; frequency 
instead of quantity is considered, and principles of the method 
of Difference may be employed in conjunction with the others. 



STATISTICS 193 

rect mistakes of memory, and so on ; as, for example, in 
matters such as the Increase or decrease of crimes, or 
the decreasing or increasing coldness of winters. 

Usually the cause discovered by means of statistics 
is only a part of the cause of the phenomenon ; the phe- 
nomenon is the result of a number of circumstances 
working together (Composition of Causes), and not al- 
ways of the same circumstances (Plurality of Causes). 

We may know already that a certain circumstance 
is causally related to a certain phenomenon but that it 
is sometimes present without the latter (through the 
agency of a Countera<^ting Cause or the absence of 
necessary supplementing circumstances). In such a 
case statistics enable us to discover how frequently, in 
what proportion of instances, the phenomenon will be 
present along with that circumstance. 

It must be remembered that the statistical method 
means more than the mere collection of cases. " With 
the collection of statistical data, only the first step has 
been taken. The statistics in that condition are only 
raw material showing nothing. They are not an in- 
strument of investigation any more than a kiln of bricks 
is a monument of architecture. They need to be ar- 
ranged, classified, tabulated, and brought into connec- 
tion with other statistics by the statistician. Then only 
do they become an instrument of investigation, just as 
a tool is nothing more than a mass of wood or metal^ 
except in the hands of a skilled workman." ^ 

The processes used in statistical investigations differ 
widely, but the following are generally given in discus- 
sions of the subject: (1) The Collection of Material, 
3 Mayo-Smith, Statistics and Sociology, p. 18. 



194 STATISTICS 

(2) its Tabulation, (3) the Summary, and (4) a Criti- 
cal Examination of its results. " In collection and 
tabulation common sense is the chief requisite, and ex- 
perience the chief teacher ; no more than a knowledge 
of the simplest arithmetic is necessary for the actual 
processes ; but since . . . all parts of an investi- 
gation are interdependent, it is expedient to understand 
the whole before attempting to carry out a part. For 
summarizing, it is well to have acquaintance with the 
various algebraic averages, and with enough geometry 
for the interpretation of simple curves, though all the 
operations can be performed without the use of alge- 
braic symbols." ^ 

The collection of statistics is carried out by various 
methods, some of them very technical ; we can note only 
a few general principles here. In the first place the 
data should be collected over a wide field. Just as in 
the non-statistical application of the inductive methods, 
it is necessary to collect data over a field wide enough 
to insure us against mistaking a coincidence for a cause 
or over-emphasizing the importance of one out of a 
number of cooperating causes, or regarding as the sole 
cause one which is onli/ one of a number of different 
causes capable of bringing about the phenomenon. 

One danger to be guarded against arises from the 
failure of different observers to use terms in exactly 
the same sense. If poverty means in some cases In- 
ability to obtain luxuries and in others, positive want, 
we can make little use of statistics of poverty. 

Again, in many statistical investigations, the data 
are obtained by means of questions addressed to a great 
^Bowley, Elements of Statistics^ p. 17. 



TABULATION 195 

many individuals ; these questions should be so worded 
as to minimize as far as possible the tendencies to care- 
less or biased observation, faulty memory, preju- 
dice, dishonesty, and imperfect description of the 
facts. 

Tabulation involves classification, and the scheme of 
tabulation should be determined by the purposes of the 
investigation — the problems which it is intended to 
solve. " In general, the scheme of investigation re- 
quires knowledge of certain groups ; and the totals re- 
sulting from tabulation should show the number of 
items in these, so that after tabulation, instead of the 
chaotic mass of infinitely varying items, we have a 
definite general outline of the whole group in question." 

The totals and averages must be so presented as to 
give a true impression to an inquirer. The subject of 
averages will be discussed more fully in a later chapter. 

In the summary, the aim is to present the results in 
the clearest, most comprehensive, and most suggestive 
way. The use of averages, and representation by charts 
and diagrams, are important here. In correlating the 
results great care is needed to avoid wrong interpreta- 
tions. An increase in the number of arrests might be 
causally related to increasing severity in the enforce- 
ment of law and not to an increase in crime. 

A critical examination of the results is possible only 
when the sources of the data, the methods of their tab- 
ulation, and the mode of summarizing and drawing 
conclusions, are fully described. 

There are, of course, many cases in which the use of 
statistics would be unnecessary : " In order to prove 
the relation between savagery and fetichism it is not 



;f 



196 STATISTICS 

necessary for us to have statistics either of economic 
condition or of religious confession. The fact stands 
out of itself simply by the consensus of observation of 
travelers and historians." ^ 

Where the law of the data is already known the fre- 
quency of their occurrence is of no further interest to 
science. The number of times an acid has combined 
with a base to form a salt is of no importance to the 
chemist. If we know the laws and the circumstances, 
the frequency of the event and the times of its occur- 
rence can easily be determined. " There was some 
Interest in counting how many eclipses of the moon and 
sun took place every year, so long as they occurred 
unexpectedly and inexplicably ; since the rule has been 
found according to which they occur and can be calcu- 
lated for centuries past and to come, that interest has 
vanished. But we still count how many thunderstorms 
and hailstorms occur at a given place or within a given 
district, how many persons die, and how many bushels 
of fruit a given area produces, because we are not in a 
position to calculate these events from their con- 
ditions." ^ 

In other cases the method of statistics may be in- 
applicable. " It is difficult to express the relation be- 
tween economic condition or religious feeling and 
aesthetic development in a civilized state, because music, 
painting, and sculpture cannot in any way be measured 
statistically. This is a question of quality and not in 
any sense of quantity." ^ 

5 Mayo-Smith, Statistics and Sociology, p. 9. 

6 Sigwart, Logic, Part III, chap, iv, 3. 

7 Mayo-Smith, loc. cit. See, however, page 210 on the ways of 
applying exact methods in investigating such phenomena. 



DIFFICULTIES IN USE OF STATISTICS 197 

The use of statistics is often severely criticised and 
there is much popular distrust of the results attained 
by their employment. There are, of course, many dif- 
ficulties to be met, and many conclusions based upon 
statistics may be false. They are liable to most of the 
errors which occur in connection with the handling of 
individual facts. The original observations may have 
been faulty ; in so far as memory was employed, further 
errors may have entered; ignorance, prejudice or inac- 
curate statements may have vitiated whatever testimony 
was employed ; the records may have been faulty or mis- 
takes may have been made in copying; the facts ob- 
served may not have been representative ; in comparing 
different groups and in noting correlations we may 
mistake a mere coincidence for causal relation. If all 
the precautions which are employed in a scientific ex- 
amination of individual facts are made use of here, 
statistics may furnish a perfectly valid basis for infer- 
ence. One practical difficulty is the unfamiliarity of 
the average reader with the use of statistics and his 
consequent inability to criticise them, and another is 
the frequent failure on the part of the investigator to 
furnish data for criticism.^ 

8 Interesting illustrations of the use of statistics are easy to 
find. The field of vital statistics is a good one for this purpose. 
One very interesting study is Dr. Allyn A. Young's A Discussion 
of Age Statistics, Bulletin 13 of the Bureau of the Census. 



CHAPTER II 

AVERAGES 

The Arithmetical Average. — -In statistical investiga- 
tions and in all others in which quantitative data are 
employed, the use of averages is often very important. 
An average is a single quantity which represents two or 
more other quantities. There are several kinds of aver- 
ages ; that with which we are most familiar is the Arith- 
metical Average. It is obtained by adding together 
the various quantities to be averaged and dividing their 
sum by the number of quantities. The weights of the 
members of a college football team were respectively, 
175, 195, 187, 183, 230, 187, 169, 147, 159, 178 and 
185. The average was 181 4-11. The average is less 
cumbersome than the whole series of quantities or their 
sum. The greater the number or size of the quantities 
the more important does the average become. 

The average tells us nothing about the individual 
cases. In this example the average is not the same as 
any single one of the quantities averaged. To take an- 
other case: the death rate of a city gives no informa- 
tion regarding the death rate of any given ward, nor 
the number of deaths in any given thousand of the 
population. An average simply serves as a means for 
representing the whole series of quantities and for com- 
paring it with other series. It gives no information 
regarding the homogeneity of the group: 180 is the 
average of 179 and 181 and also of 359 and 1. 

There are many cases in which the simple form of the 

198 



THE WEIGHTED AVERAGE 199 

arithmetical average or mean is inadequate ; sometimes 
a modified form of it can be used. 

The *^ Weighted" Average.— Suppose we know that 
of six groups of men the average weights are respect- 
ively 180, 148, 172, 164, 156 and 152 pounds. The 
average is 162. Can we say that this average satis- 
factorily represents the whole series of groups .^^ That 
will depend upon the circumstances. If the groups 
were of approximately the same size it might be suffi- 
cient, but if in the first group there were 10 ; in the 
second, 200 ; in the third, 50 ; in the fourth, 20 ; in the 
fifth, 100; and in the sixth, 150, our average will be a 
very imperfect representative of the groups. If, on 
the other hand, we multiply each of the averages in the 
series by the number of individuals in the group which 
it represents and divide the sum of these products by 
the total number of individuals, we get the average 
154 6-53, which is much more accurate than that first 
given. 

180x10+148x200 + 172x50 + 164x904-156x100 + 152x150 _ / 
10 + 200 + 50 + 20 + 100 + 150 ^^^ 

This is an illustration of what is known as a weighted ^ 
average ; it is a special form of arithmetical average. 
Where the groups represented by a series of averages 
vary greatly in size we have conditions which call for 
" weighting the averages." " The classical and most 
useful application of weights is the formation of an 
index-number for the change of prices by fitting suit- 
able weights to the changes measured in the prices of 
various commodities. It is required to find the change 
in the value of gold when measured by the prices of 
other commodities. Suppose that we are given that 



200 AVERAGES 

prices of certain commodities between two years were 
in the following ratios : 

Wheat Silver Meat Sugar Cotton 

First year 100 100 100 100 100 

Second year 77 60 90 40 85 

The simplest way to estimate for the general fall 
in price is to take the simple average of the numbers 
in the second year, viz., 70.4, and say that the general 
prices in the second year were 70.4 : 100 ^ when ex- 
pressed in commodities. But it is at once clear that 
we can not allow the commodities given to have equal 
influences on the result ; wheat is of greater importance 
than sugar and meat than silver; and again we have 
taken arbitrarily three items to represent food and one 
for clothing; we need some means of deciding relative 
importance. Suppose we decide that wheat, cotton, 
meat and sugar are respectively 7, 4, 3, times and twice 
as important as silver, we should get the following 
table : 

Commodity Relative prices Weight Product 

in second year Assigned 

Wheat 77 7 539 

Silver 60 1 60 

Meat 90 3 270 

Sugar 40 2 80 

Cotton 85 4 340 



352 17 1289 

1289 
Weighted average is =75.8 

17 

352 

Unweighted average is ^=70.4 ^ 

5 

1 That is, prices of commodities have fallen in this rate or the 
value of gold has increased correspondingly. 

2 Bowley, Elements of Statistics, pp. 111-11^. 



THE MODE 201 

It IS not always easy to tell what weights should be 
assigned, but considerable variation is possible without 
much modification of the result. 

The Mode. — ^Another sort of average which is often 
of great importance is what is known as the Mode. It 
is that quantity which occurs with the greatest fre- 
quency. It is what we frequently have in mind when 
we speak of the average man, the average student, etc. 
If in a class of students, 10 receive the grade A; 20, 
the grade B; 50, the grade C; 100, the grade D; and 
25, the grade F, the mode is D. The mode very often 
represents the type more accurately than does the aver- 
age. It gives us no information about any one indi- 
vidual, but it does indicate the sort of individual which 
occurs more frequently than any other sort. There 
might well be two or more modes in a given series of 
quantities. If a class were made up of very bright and 
very dull students, the numbers receiving the various 
grades might be A, 25 ; B, 50 ; C, 20 ; D, 100 ; and F, 
25. The two modes are at B and D. 

The mode is not always easy to determine. In these 
examples the grade B, for instance, means a range be- 
tween the grade which is just high enough to escape 
C and that which is the smallest fraction short of A. 
It might well be that of the 50 who were in C, 35 were 
in the lower half of the group, while of those that were 
in D 80 were in the upper half of the group, so that the 
mode was really in a group which might be indicated by 
the expression D +, C -. The degree of accuracy re- 
quired in the results would determine the degree of 
exactness with which we should state the mode. 

The mode is often most useful. " The mode rather 
than the average in chest-measurements is the number 



202 AVERAGES 

most suitable for the ready-made clothier. For pro- 
viding a post-office or a store, the mode in postal-orders 
or prices of tea needs to be known rather than any other 
average. Even the favorite coin in a collection may 
show the spirit of the congregation better than the 
arithmetic average of their contributions." ^ 

If the series under consideration is very irregular it 
may be quite impossible to apply the mode. 

The mode has this advantage over the arithmetical 
average: it is uninfluenced by extreme cases. In the 
illustration on page 198, the average weight of the 
players would be considerably changed if a player 
weighing 180 pounds were substituted for the one 
weighing 230 ; let us see what would happen in the case 
of the mode. More of the quantities fall between 180 
and 189 than within any other equal range. This 
range, 180-189, then, will be the mode. The substitu- 
tion of the lighter player does not modify the mode. 
Where the number of quantities is so small as in this 
illustration, the individual quantities are often men- 
tioned, but where that is not the case, the mode is often 
useful either as a supplement to the arithmetical aver- 
age or as a subsitute for it. 

The Median. — Another kind of average useful in 
many cases is the Median. The Median is the middle 
quantity in a series. The weights of the players, in 
the order of their magnitude, were 147, 159, 169, 175, 
178, 183, 185, 187, 187, 195, 230. The median is 183. 
There are just as many items above it as there are 
below. The median, like the mode, is unaffected by ex- 
treme cases. " The existence of any number of million- 
aires has no more effect on the median income than of 
3 Bowley, Elements of Statistics, p. 1^3o 



THE MEDIAN 203 

an equal number of other persons whose incomes are 
above the median.'' ^ The median is very easy to find, 
since it is only necessary to arrange the items in the 
order of their magnitude and find which occupies the 
middle position. If there is an even number of items 
the median lies between the two middle ones. Even if 
our information regarding the items is incomplete it is 
often possible to find the median with a fair degree of 
accuracy. " It may be that in the ' wage census ' 
100,000 persons whose wages were far below the aver- 
age did not come into the returns at all, and it is very 
difficult to estimate their eff*ect on the arithmetical aver- 
age, for want of information as to their earnings ; but 
to find the median exactly we need only know their num- 
ber, not their earnings ; and if we can assign a maximum 
for their number, we still can place the median within 
narrow limits." 

One great advantage in the use of the median is to 
be found in the fact that it can be employed in dealing 
with quantities for which no accurate measurements X 
can be obtained. This is especially important in deal- 
ing with psychological phenomena. We may be able 
to say that A has a better memory than B without being 
able to measure either, or to state the exact amount 
in which A is superior to B. The members of a class of 
any size might be arranged in the order of their excel- 
lence in any quality whatever and the median found as 
in the case of numbers. Francis Galton, in his Natural 



4 "The magnitudes one-quarter and three-quarters up the series 
are called the quartels; those one, two, .... nine-tenths of the 
way up are the deciles; those one, two, .... ninety-nine hun- 
dredths up are the percentiles," Bowley, Elements of Statistics, 
p. 124. 



204 AVERAGES 

Inheritance and in other works, developed and applied 
this type of average with great effectiveness. 

The median may be a very imperfect representative 
of the type. If, in a group of 100 men, the weights of 
50 were between 190 and 210 pounds, while the others 
ranged between 130 and 150 pounds, the median would 
be 170. " The median is then chiefly useful when we 
are dealing with a series of objects of which the main 
part lie fairly close together; a few extremes do not 
affect it." ' 

The Geometrical Average.— Another kind of average 
useful in certain cases is the Geometrical average. It 
is related to the arithmetical average somewhat as com- 
pound is to simple interest. The population of Great 
Britain and Ireland increased from 12 millions in 1789 
to 38 milUons in 1890. Obviously it would be unsafe 
to say that the average increase was the total increase, 
26 millions, divided by the number of years. We should 
expect the annual increase to be greater as the popula- 
tion became larger, and, other things being equal, the 
two would vary together. When we have only two 
quantities to deal with, the geometrical average is easily 
found. In such a case it is the mean proportional. The 
geometrical average of 4 and 16 is 8. The geometrical 
average of 5 and 9 is the square root of 45, or 3 
into the square root of 5. If we were dealing with 
three quantities the geometrical average would be the 
cube root of their product ; if with five, it would be the 
fifth root of their product ; the general formula for n 
quantities is the n\h root of (X^ «2 • • • • ^n" With large 
or numerous quantities logarithms should be used. The 
name logarithmic mean is sometimes employed for this 
5 Bowley, Elements of Statistics, p. 1^6. 



THE GEOMETRICAL AVERAGE 205 

kind of average. The geometrical or logarithmic mean 
IS a quantity which can be substituted for each of the 
quantities when they are multiplied together and give 
the same product, whereas the arithmetical mean is one 
which can be substituted for each of them when they 
are added together. " Which mean we should choose is 
simply a question of which we believe will best represent 
the facts. If the growth of cities depended altogether 
upon the birth of children within their boundaries, we 
should naturally choose the geometrical mean, for the 
larger the city (other things being equal) the more 
children will be born in it. If, on the other hand, the 
population of a city, like that of a prison or hospital, 
were made up altogether of certain kinds of people 
who were sent there from without, there would (?) be 
no reason why a large city should gain more inhabi- 
tants than a small one ; and the more appropriate aver- 
age would be the arithmetical. With most cities the 
natural rate of growth is only partly geometrical and 
partly arithmetical ; so that neither a series of means 
of the one sort nor a series of the other would give a 
wholly satisfactory representation of the mean growth 
from year to year between one census and another. If 
in any case or set of cases we have reason to believe 
that the true mean lies somewhere between the arith- 
metical and the geometrical, and if we wish to represent 
the facts as accurately as they can be represented by 
any mean, we must take a mean that does lie between 
the two." ' 

Measuring Deviations from an Average. — It is often 
important when using averages to know something 
about the closeness with which the several quantities 
6 Aikins, The Principles of Logic, p. 315, 



206 AVERAGES 

approximate the average. Suppose for example, that 
we had a number of different measurements of a given 
quantity, say the distance between two points: if there 
was httle variation among the measurements we should 
usually regard their average as a fairly accurate repre- 
sentation of the real quantity ; but if the variation were 
very great we might have little or no confidence in the 
average. We shall need some way of indicating the 
amount of divergence within the group, or, in other 
words, the closeness with which the several quantities 
were grouped about the average. 

1. One simple way of doing this is to take the aver- 
age of the deviations from the mean or average. Eight 
is the average of 5, 6, 11, and 10, and also of 1, 2, 15, 
and 14. The deviations in the first series are 3, 2, 3, 
and 2. The average of these deviations is ^% or 2/4. 
The deviations in the second series are 7, 6, 7 and 6 ; 
the average deviation is 6/4. 

(The deviations are technically known as " errors," 
and their average as the Average Error,) 

The smaller the average error the more closely are 
the quantities grouped about the average ; and the more 
closely they are grouped about the average the more 
homogeneous is the group. 

2. Another kind of average frequently employed in 
this connection is the Median or Probable Error (P. 
E.). Arrange the errors in the order of their magni- 
tude ; the Median of these will be the so-called Probable 
Error, or the quantity within which half of the errors 
fall. Thus, if we have the quantities, 1, 3, 6, 8, 9, 12, 
13, 15, 16, 17, the average will be 10. The errors will 
be 9, 7, 4, 2, 1, 2, '3, 5, 6, 7. Arranging these in the 
order of their magnitude we have 1, 2, 2, 3, 4, 5, 6, 7, 7, 



PROBABLE ERROR 207 

9. The median will fall between 4 and 5, i. e., 4%. In 
other words, 4% is the quantity below which half the 
errors fall and above which we will find the other half. 
Assuming that our data are representative of the class 
of facts for which they stand, any new number standing 
for things in the same class is as likely to be within 
4^ of the average as it is to be beyond it. Exactly half 
of the quantities already determined lie within that 
range (in the example, between the numbers 5% and 
14%), and those already determined are, according to 
our supposition, selected from a wide enough field to be 
regarded as representative of the whole. An average 
of 10 with a probable error of 4.5 means a series of 
quantities in which there is a wide range of variation. 
An average of 100 and a P. E. of .1 would indicate 
a very homogeneous group. In the case of measure- 
ments it would mean that there was a close agreement 
among the different measurements and that the average 
was therefore a fairly accurate approximation to the 
true measurement (providing, of course, that constant 
errors had been eliminated). 

" An approximation to the probable error for a 
given series of observations is obtained by arranging all 
the observations in order of magnitude ; marking the 
magnitude, say a, above which 25 per cent, of the ob- 
servations lie, and the magnitude, say b, below which 
25 per cent. lie. Half the difference between a and b 
is the probable error. A useful way of illustrating this 
is to say that if one observation is chosen at random 
out of a group, it is as likely as not that it will not 
lie further from the average than the probable 



error.'' ^ 



7 Bowley, Elements of Statistics, p. 2S9, 



208 AVERAGES 

Measurement of Phenomena. — In the more advanced 
stages of most sciences the exact measurement of phe- 
nomena becomes more and more important. To deter- 
mine the relations of a phenomenon it is not only 
necessary to know when it happens and what its accom- 
paniments are, but also how much of it is correlated 
with given amounts of other phenomena. This is evi- 
dent in the employment of the methods of Concomitant 
Variations, for this method deals with cases in which 
the quantity of the phenomenon varies. In the method 
of Residues also, quantitative measurements are of great 
importance ; indeed, they are usually necessary. We 
observe how much of a given phenomenon is due to one 
cause, how much to a second, and so on ; the remainder 
is due to something else not previously known to be a 
cause, etc. 

The physical sciences are very largely quantitative, 
and more recently biology has come to employ the 
methods of exact measurements in many of its investi- 
gations.^ Measurement usually means the employment 
of instruments. Measurements of magnitudes by the 
unassisted eye are exceedingly inexact, and measure- 
ments of degree of quality are even more so. White 
marble painted in a picture representing an architec- 
tural view by moonlight seems to be of about the same 
degree of brightness as the actual moonlit marble would 
be, but Helmholz has calculated that it is from ten to 
twenty thousand times as bright.^ 

To make measurements it is necessary to fix units in 

8 The name of Karl Pearson is most closely associated with 
" Biometry." 

» James, Psychology ^ Briefer Course, p. 155. 



MEASUREMENT 209 

terms of which the magnitudes are to be expressed. 
These are usually determined arbitrarily. Units, stand- 
ards, and instruments of measurement vary with the 
phenomena to be measured and can not be discussed 
further here/^ 

Many errors may occur in making measurements, and 
although it is often possible to eliminate some of them, 
in the vast majority of instances the measurement is 
almost certainly inexact. Repeated measurements are 
very seldom in exact agreement. If phenomena were 
broken up into units of uniform magnitude there would 
be less difficulty, but most phenomena are continuous. 
Time is not broken up into minutes, and with the most 
exact instruments it is impossible to say when a minute 
has passed. It can be determined within millionths of 
a second but not with absolute exactness. For most 
practical purposes rough measurements are sufficient ; 
thus, for the train dispatcher it may be enough to deter- 
mine the time to a second, but for astronomical calcu- 
lations the smallest possible error may be of serious 
importance. Most measurements are only approxi- 
mately true ; the problem is to make the approximation 
as close as possible. 

There are various conditions to be observed and 
various methods which can be used in attempting 
to get exact measurements, but they are too technical 
to be included here.^^ Constant errors, such as the 
personal error,^^ can often be determined and allowance 
can be made for them. But after all such allowances 



10 See Jevons, Principles of Science, chap. xiv. 

11 See Jevons, Principles of Science, chap. xiii. 

12 See page 2S. 



210 AVERAGES 

have been made and after all the means for avoiding 
and minimizing error have been employed, there yet 
remains a margin of uncertainty. In such cases it is 
possible to obtain a close approximation to the true 
measurement by taking a number of measurements and 
striking an average. After constant errors have been 
eliminated any given measurement is as likely to be too 
great as it is to be too small ; hence, in a large number 
of measurements there will probably be as many of 
those which exceed the true magnitude as there are of 
those which fall short of it. If the number of measure- 
ments Is small this is more doubtful, but if a great many 
measurements have been made, we can rely upon the 
average with safety. The average of all these measure- 
ments is the closest approximation which we can get. 
Different kinds of average are used according to cir- 
cumstances. The closeness with which the several meas- 
urements are grouped about the average will be 
indicated here, as in all cases of the use of 
average, by the size of the error. If the error is 
small, the measurement is reliable, if large, more doubt- 
ful. 

The Comparison of Quantities which Cannot be 
Measured. — In the study of many phenomena the prob- 
lem of quantitative comparison is made very difficult by 
our inability to find an exact quantitative equivalent 
for the phenomena. " Many mental phenomena elude 
altogether direct measurement in terms of amount. How 
many thefts equal in wickedness a murder? If the 
piety of John Wesley is 100, how much is the piety of 
St. Augustine? How much more ability as a dramatist 
had Shakespeare than Middleton? What per cent, must 



COMPARISON OF QUANTITIES 211 

be added to the political ability of the Jewish race to 
make It equal to the Irish race? . . . Nevertheless, 
such phenomena can be measured and subjected to quan- 
titative treatment." ^^ 

The method to be employed In such cases, as Pro- 
fessor Thorndike goes on to show. Is to arrange the 
individuals (or other unmeasurable data) according to 
their rank. We may not be able to say how much 
more eminent A Is than B, but if we can say that A Is 
in the first rank, whereas B Is in the tenth, we have a 
true basis of comparison. We cannot measure directly 
the intelligence of students in a class, but we may be 
able to say that one Is In. the first group, whereas an- 
other is in the fourth. Thus, with any number, it would 
be possible to give each his proper place In the group. 
This method can be applied to any trait whatever. The 
great difficulty Is In making sure that the ranking Is 
correct. Single observations and individual judgments 
are subject to the same errors here as in all other cases 
of observation. 

EXERCISES. 

1. What sort of average should be employed in deter- 
mining the standard size of an article to be manufactured 
in large quantities— say window shades? . ,, 

2. What sort of average should be employed in getting 
a number to represent the value of articles in a large and 
varied invoice of merchandise? 

3. If a college had 400 students in 1880 and 1000 stu- 
dents in 1905^ how many did it have in the year which falls 

13 Thorndike, An Introduction to the Theory of Mental and 
Social Measurements^ p. 18. This book is an exposition of the 
methods of measuring individuals, groups, variability of perform- 
ances, etc., including an exposition of the necessary modes of 
presenting the facts, making calculations, and so oa 



212 



AVERAGES 



half way between_, provided that the rate of increase was 
constant ? 

4. What averages might be employed and which would 
be preferable in comparing the stature of soldiers in the 
French army with those in the American army? In cora- 
paring the standing of successive classes in college? " In 
comparing the salaries of members of the faculty in two 
universities? In comparing the rate of growth of a large 
university and a small college? 

5. How would you indicate the degree of closeness with 
which a series of quantities approached their average? 

6. What is the difference between *' Average Error " and 
** Probable Error? '' 



i 



\a)- 



CHAPTER III 
PROBABILITY 

The conclusions at which we arrive by the assistance 
of statistical methods and the employment of averages 
often fall far short of the certainty attaching to scien- 
tific laws. The conditions required for establishing a 
scientific law are not fully present, and consequently 
many of such conclusions, if not all of them, lack com- 
plete verification. It does not follow, however, that 
these are valueless. As a matter of fact, most of the 
generalizations which we use in everyday life are in- 
completely verified; they are extremely valuable as in- 
struments of knowledge and practice ; indeed, in the 
absence of scientific laws, they are indispensable. So 
long as their provisional character is remembered, there 
is no serious danger in using them. 

A generalization of this character is said to be prob- 
able or to possess some degree of probability. Proba- 
bility belongs also to particular propositions. What do 
we mean by probability, — ^by saying that a statement is 
probably true, — that an event will probably happen? 
As we use the term ordinarily, it means that we believe 
we have a right to accept a statement or expect an 
event, without feeling perfectly certain of it. This 
attitude, when it has any justification, is based upon the 
belief that the grounds for accepting the statement are 
stronger than those for rejecting it. It may be that 
we know of no positive reasons against it, but do not 
regard the reasons in its favor as conclusive ; or it may 

213 



SI 4 PROBABILITY 

be that there are positive reasons against it, but that 
those in its favor are stronger or more numerous. These 
reasons or grounds may be of various kinds. There may 
be many things pointing toward the occurrence of 
such an event ; as, for example, in the statement that 
life will probably at some time cease upon the earth. 
Or conditions at the present time may be similar to 
those in which the event has happened before ; the out- 
come of an examination of instances according to the 
principles of the method of Agreement gives a result 
which is usually only probable. In all these cases it 
is impossible not to feel that a great deal of vagueness 
attaches to our statement that anything is probable. 
We are not able to say how probable it is. There is 
such a thing, however, as mathematical or quantitative 
probability. It is based upon the comparative number 
of times an event or connection of events has occurred. 
If a given circumstance A has been observed 1000 times, 
and if, in 700 cases of its occurrence, a phenomenon B 
has also been present, we have definite grounds for in- 
ferring that A will probably be accompanied by B 
again. Every time A and B have occurred together 
in the past is an argument in favor of their occurring 
together in the future, and every time A has occurred 
without B is an argument against this connection ; if 
the cases of the latter sort are many in comparison with 
those of the former, we say that the connection in the 
future is improbable. In the case just mentioned we 
should express the degree of probability by the frac- 
tion %o. Now in dealing with the matter in this quan- 
titative way, the term " probability " has a meaning 
which is somewhat different from that in which we 



THE MEANING OF PROBABILITY 215 

ordinarily use it. It would mean, in the present case, 
that in the future we should have a right to expect B 
along with A in seven cases out of ten. It means noth- 
ing with regard to the next case; we have no more 
reason for expecting one outcome than the other ; our 
information has value only for the long run ; we have 
no right to expect that in the next ten cases B will be 
present seven or any other particular number of times ; 
but in the long run we may expect this proportion to 
hold and the longer the run the closer is the approxi- 
mation which we may expect. 

Compare this with one of the former illustrations, 
" Life will probably cease upon the earth." That does 
not mean that in a large number of cases of the sort 
before us life would cease in most of them ; we are here 
dealing with the particular case and all our arguments 
apply to it. In quantitative probability we know noth- 
ing of the circumstances of the particular case ; it is 
simply one of a certain group, and certain members 
of this group behave in one way, whereas others behave 
in a different way, and we cannot determine the circum- 
stances of their behavior in either case. The fraction 
expressing the degree of probability tells us that, in 
the past, the phenomenon has appeared in connection 
with a certain circumstance in such and such a pro- 
portion of cases and that we may, unless there are 
reasons to the contrary, expect this proportion to hold 
in the future. (We proceed here as elsewhere, upon 
the assumption that the future will be like the past and 
that any set of phenomena will behave in the future as 
it has in the past, in the absence of any new and dis- 
turbing factor.) 



216 PROBABILITY 

Probability, in this connection, does not necessarily 
mean favorable odds. The event may have occurred in 
only one-tenth of the cases ; its probability will then be 
YiO' If it has occurred in one-half the number of cases, 
the probability will be %, etc. 

The calculations of insurance companies are based 
upon data showing the number of deaths per year for 
individuals of various ages, and so on. The great value 
of vital statistics and of statistics of many other sorts 
is to enable us to determine the probability of events 
which we cannot bring entirely under laws. 

Deducing the Probability of a Phenomenon. — There 
are certain circumstances in which the probability of a 
phenomenon may be determined deductively. For ex- 
ample, we can say at once that in tossing a coin the 
probability of getting heads is % ; we know that there ^ 
are two possibilities and only two ; if the coin is prop- 
erly made we know of no reason why one side should, 
in any particular case or in the long run, fall any 
oftener than the other.-^ 

We say that their chances are equal and that the 
probability of each is /4. In the cgise of a die the proba- 
bility that any specified side will come uppermost is %. 
There are six possibilities, all equal. In the long run 
we expect each side to turn up as frequently as any 
other, viz,^ in one-sixth of the cases. The chances of 
any one are as 1:5; one for, and five against. If we 
have a bag containing twenty balls, three of which are 
white and the rest black, the probability of drawing a 
white ball is /4o. In this instance there are twenty pos- 

1 It is essential in such calculations that there be no known 
factor favoring a given result more than any other. 



DEDUCING PROBABILITY 217 

sibilities, three of which would give the desired result ; 
drawing a white ball may be brought about by realizing 
any one of three possibilities ; or, out of twenty possi- 
bilities, three are favorable. In instances of this sort 
we have a definitely known number of possibilities, with 
no reason to believe that there is anything tending to 
bring about one rather than another. The probability 
of any specified one among them will be expressed by 
a fraction having 1 as its numerator and the number 
of possibilities as its denominator. In the case last 
cited the probability of drawing any particular ball is 
%o- If among these possibilities any number of them 
favor the realization of any particular phenomenon, the 
probability of that phenomenon will be expressed by 
a fraction having as its denominator the total num- 
ber of possibilities and as its numerator the number of 
possibilities favorable to the occurrence of the phe- 
nomenon in question. If all the possibilities were fa- 
vorable (e. g,^ if all twenty balls were white), the frac- 
tion would be ^%o or 1, which is the symbol for cer- 
tainty, or the upper limit of probability ; if none were 
favorable, it would be %o or 0, the lower limit, or im- 
possibility. 

Suppose we toss the coin twice (or toss two coins), 
what is the probability of getting heads both times .^ 
There are four possibilities, as follows: 

H H 

H T 

T H 

T T 



218 PROBABILITY 

We might get heads in both, or heads in the first 
and tails in the second, or tails in the first and heads in 
the second, or tails in both. In only one of these does 
heads come in both throws; the probability is therefore 
%. It is the same for two tails. For one heads and 
one tails it is %. For heads in the first throw and tails 
in the second it is again /4, and so on. 

If we should toss it three times, the probability of 
getting heads each time would be %. There are eight 
possibilities : 

H H H T H H 

H H T T H T 

H T T T T H 

H T H T T T 

We can get the probability/ for any number of throws 
by multiplying together the probabilities for each of the 
several throws; for two throws, % x%, or /4; for three, 
y2 X 1/4 X Y2, or Vs ; for five, V2 x % x 1/2 x % x 1/0, or V^2, 
and so on. The results would be the same if we should 
throw several coins at once instead of throwing one 
several times. Suppose we are drawing balls from two 
bags ; one of them contains three white and seventeen 
black balls ; the other contains two white and eight 
black balls. What is the probability of drawing a 
white ball from each? The probability, in one case, is 
/4oj and in the other %o ; the probability of getting a 
white from each is therefore %oo or %oo. Each in one 
bag might be drawn with any one in the other ; hence 
there are 200 possibilities, only six of which are favor- 
able ; each of the two whites in one bag might be drawn 
with each of the three in the other. 



, DETERMINING PROBABILITIES 219 

The probability of getting any combination of in- 
dependent events is thus obtained by taking the product 
of the probabilities of the several events. 

If two events are mutually exclusive the probability 
of getting one or the other would be the sum of their 
independent probabilities. In tossing a coin, the prob- 
ability of getting heads is % and that of getting tails 
is the same ; the probability of getting one or the other 
is the sum of the two or 1 = certainty. In throwing a 
die, the probability of getting a five is %, the proba- 
bility of getting a six is the same, the probability of 
getting one or the other is %. 

In tossing a coin twice, " It might be argued that 
since the probability of throwing heads at the first 
trial is /4 and at the second trial also %, the 
probability of throwing it in the first two throws 
is 1, or certainty. The true result is %, or the proba- 
bility of heads at the first throw, added to the exclusive 
probability that if it does not come at the first, it 
will come at the second." ^ The probability that it will 
come in the first is ■J/2. The probability that it will not 
come in the first is also % ; the probability that It will 
come in the second is also %. The product of the two 
last gives the probability that if it does not come In the 
first, it will in the second. This product, added to the 
first %, gives the probability that it will come In at 
least one of the two throws. There are, of course, four 
possibilities in two throws, and three of them give at 
least one heads. 

If we represent the probability that an event will 
happen by p, then the probability that it will not hap- 

2 Jevons, Principles of Science, chap, x, 3. 



220 PROBABILITY 

pen is 1 — p. The probability in throwing a die that 
five will not come up is 1 - % or %. 

Let us suppose a case in which six coins are tossed 
(or in which one coin is tossed six times) ; what are the 
probabilities of 6, 5, 4, 3, 2, 1 and heads respectively? 
There will be 64 possibilities, as follows: 

6 

HHHHHH TTTTTT 

5 1 

HHHHHT HTTTTT 

HHHHTH THTTTT 

HHHTHH TTHTTT 

HHTHHH TTTHTT 

HTHHHH TTTTHT 

THHHHH TTTTTH 

4 a 

H H H H T T H H T T T T 

HHHTTH THHTTT 

HHTTHH TTHHTT 

HTTHHH TTTHHT 

TTHHHH TTTTHH 

HHHTHT HTHTTT 

HHTHTH THTHTT 

H T H T H H T T H T H T 

THTHHH TTTHTH 

HHTHHT HTTHTT 

HTHHTH THTTHT 

THHTHH TTHTTH 

HTHHHT HTTTHT 

THHHTH THTTTH 

THHHHT HTTTTH 



PROBABILITY 221 

3 3 

HHHTTT HHTHTT 

HHTTTH HTHTTH 

H T T T H H T H T T H H 

TTTHHH HTHHTT 

HHTTHT THHTTH 

HTTHTH THHTHT 

T T H T H H T H TH H T 

HTTHHT THTHTH 

TTHHTH HTHTHT 

TTHHHT THHHTT 

One combination gives six heads, six give five, etc. 
The probabihties for 6, 5, 4, 3, 2, 1, and heads are 
respectively %4, %45 ^%4, ^%4, ^%45 %4, %4. In ten 
throws the number of posslbihtles would be 1024; the 
numbers favoring 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and 
heads would be respectively, 1, 10, 45, 120, 210, 252, 
210, 120, 45, 10, 1. Examination will show that these 
series of numbers (1, 6, 15, 20, etc., and 1, 10, 45, 120, 
etc.) are the coefficients of the terms of a binominal 
raised to the power indicated by the number of throws 
(6, 10, etc.). In these cases the phenomena are not mu- 
tually exclusive. The fact that heads comes (or does 
not come) in any throw makes no difference to the other 
throws. 

There are important scientific applications of the 
facts just brought out.^ " Suppose, for the sake of 
argument, that all persons were naturally of the equal 
stature of five feet, but enjoyed during youth seven 
independent chances of growing one inch in addition, 
1 Jevons, Principles of Science, chap, ix, 5. 



222 



PROBABILITY 



Of these seven chances, one, two, three, or more, may 
happen favorably to any individual; . . . out of every 
128 people: — 



1 person would have the stature of ,5 feet inches. 

7 persons 
21 
35 
35 
21 

7 

1 






5 




1 




5 




2 




6 




3 




5 




4 




5 




5 




5 




6 




5 




7 





The probability of a stature of 5 feet 1 inch would be 
%285 the whole number of possibilities being the de- 
nominator. 

There are sometimes cases in which an event has hap- 
pened in all the instances in which a given circumstance 
or set of circumstances has been present — B has always 
followed A. What is the probability of its happening 
the next time the circumstance or circumstances recur? 
Let the number of times it has happened be represented 
by m. Then the probability of its happening the next 
time is expressed by the fraction ^^^^44« This may 
be determined by a series of mathematical operations or 
more simply as follows : " In this fraction the de- 
nominator represents the sum of conceivable cases, since 
after m real cases have occurred there are always two 
additional cases, which we can think of as occurring, 
viz,, the repetition or non-repetition of E (the event) ; 
the numerator as usual denotes the number of favorable 
chances. The example usually adduced is that as the 



DANGERS TO BE AVOIDED 223 

alteration of day with night has now been historically 
attested for 5,000 years, the probability of the same 
alternation recurring to-day = 1,826,214 : 1,826,215 ; 
that is, one may bet 1,826,214 to 1 on its occurring 
again. "^ 

Dangers to be Avoided in Interpreting Proba- 
bilities. — Care is needed in the employment and inter- 
pretation of probabilities. When we say that the prob- 
ability of heads is z^, we do not mean that in two throws 
we shall get heads once, nor do we mean that in any 
definite number of throws the number of heads and tails 
will be equal. Indeed, a run of heads of any finite length 
is possible. The probability of a run of ten is /4o24. 
But the longer the series the more closely should we 
expect the proportion of heads to approximate that in- 
dicated by the statement of its probability. If heads 
have come up four times already the probability of their 
coming up the next time is still % ; the same is true if 
they have come up ten or any other number of times. 
The past throws have nothing to do with the present 
or future. To expect that, because a coin has come up 
heads several times in succession, it is therefore more 
likely to come up tails the next time,^ is wholly to mis- 
understand the meaning of probability. Indeed, a pre- 
ponderance of heads in the past throws would suggest 
that the coin was not true, that there was a hidden 
cause favoring heads, and that as a matter of fact the 
probability of heads was greater than %. In no case 
does the knowledge of the probability of an event give 
any definite information regarding the next or any other 

3 Lotze, Logic, Book II, chap. 9. 

4 This is sometimes called the " gambler's fallacy." 



224 PROBABILITY 

specified case. It simply tells us that in the long run 
we have a right to expect a certain proportion of oc- 
currences, and the longer the run, the closer the ap- 
proximation. So far as " luck," pure and simple (fav- 
orable or unfavorable accident). Is concerned, we might 
expect that. In the long run, and taking an Infinite num- 
ber of Individuals, " good luck " and " bad luck " would 
be equal, though particular individuals might be always 
lucky or unlucky, or their good or bad luck might begin 
or end at any point whatever. Bad luck In the past 
would be no evidence of bad luck in the future. Of 
course, a great deal that we ordinarily call luck or 
chance is really the result of ability, foresight, and so 
on, or of their opposltes. 

EXERCISES. 

1. What does each of the following propositions mean? 

(1) He is probably an official of some sort. 

(2) There is a strong probability in favor of his 

being elected. 

(3) The probability of ten more years of life for a 

man of his age is %. 

2. " The probability that a new-born child will live to 
the age of 25 years is %; and if it lives to that age^ the 
probability of its being well-educated is %; and if it is 
well-educated^ the probability of its being a distinguished 
person is %o« Calculate the probability of the new-born 
child's being a distinguished person." — Ray^ Logic, 

S, Thirty per cent, of the men in college are Freshmen^ 
and twenty per cent, of the Freshmen come from the West. 
What is the probability that the next student who passes 
will be a Freshman from the West? A Freshman and not 
from the West ? Not a Freshman ? 

4. What is the probability that a die will fall •with the 
same side up five times in succession ? \ ^ 

K 



EXERCISES 225 

5. What is the probability that a given side of a die. 
will come up at least once in two throws ? In three throws ? ^-^ 

6. In tossing a coin four times^ what is the probability 
of getting heads three times? 

7. Suppose that an event had happened in one thousand 
cases in which a given phenomenon had been present and 
had never failed to happen when the latter was present; 
what would be the probability of its happening when next 
the phenomenon was present? 







SUPPLEMENT TO PART II 



THE GRAPHIC METHOD OF REPRESENTING 
DATA AND THEIR RELATIONS 

When large groups of figures are to be presented 
it is often useful to employ diagrams which will enable 
the eye to grasp at once the series as a whole. There 



G. Britain. .1,633,000 

U. S 611,500 

France 609,000 

Germany 529,000 

Japan 374,000 

Russia 207,500 

Austria 113,000 

are many varieties. Pop- 
ular discussions of com- 
parative populations, 
wealth, navies, and so on, 
often represent the var- 
ious figures by lines or 
surfaces which are so 
juxtaposed as to show at 
once to the eye the rela- 
tions of the several quan- 
tities. Thus, the ton- 
nage of the eight great- 
est navies of the world in 
1907 was approximately 



A. 



Fig. 1 



R. 



J. 



G. 



U.S 



G.B. 



Fig. 2 



226 



THE GRAPHIC METHOD 



227 



as above. Or we might employ rectangles with equal 
bases, or points on a curve. 

The relation between two series of numbers or quan- 
tities may be represented graphically. Let us take a 
case in which successive quantities are related to suc- 
cessive years. The population of the United States 
at each census, from 1820 to 1900, was approximately: 
1820, 9 millions; 1830, 12 millions; 1840, 17 millions; 
1850, 23 millions ; 1860, 31 milhons ; 1870, 38 miUions ; 
1880, 50 millions; 1890, 62 milhons; 1900, 76 millions. 
These facts could be represented thus: 



ou 
O 


















(76) 
















(62) 


«60 

P. 50 
C 

^^0 
















(50) 
















(38) 








o 

m 30 

O 










(31) 














(23) 












•r-l 

S 10 


(9) 


(12) 


(ly; 































Years 1820 '30 '40 '50 '60 '70 '80 '90 1900 
* Fig. 3. 



ou 

s'" 

T! 60 

cd 

1.50 
O 

^40 
O 
to 30 

;§ 20 

r—t 

§10 


















/ 
















A 


V 
















/ 
















/ 


^ 












A 


/ 














^ 


y 












^^ 


^ 


< 












^ 


tl"^ 

















Years 1820 '30 '40 '50 '60 '70 '80 '90 1900 

Fig. 4. 



228 DATA AND THEIR RELATIONS 

In the first figure the successive quantities are repre- 
sented by rectangles with equal bases, the years being 
indicated on the base line and the population on the 




o 
o 



Fig. 5. 



vertical. Or we can indicate the quantities by a series 
of points located according to their size and date and 
join these points by a curve, as in figure 4. 



AN ILLUSTRATION 229 

Figure 5 is borrowed from Bowley's Elements of 
Statistics, and represents the following data: 

SHILLINGS 

Numbers of work people earning from 15 to 16 — 200 

" 16 to 17— 400 

" 17 to 18— 100 

" 18 to 19— 100 

" 19 to 20— 200 

" 20 to 21— 200 

" 21 to 22— 300 

" 22 to 23— 300 

" 23 to 24— 500 

" 24 to 25— 900 
" 25 to 26 — 1200 

" 26 to 27— 800 

" 27 to 28— 700 

" 28 to 29— 500 

" 29 to 30— 300 

" 30 to 31— 300 

" 31 to 32— 400 

" 32 to 33— 400 

" 33 to 34— 500 

" 34 to 35 " 500 

" 35 to 36— 600 

" 36 to 37— 400 

" 37 to 38— 100 

" 38 to 39— 80 

" 39 to 40— 20 

Median, 26/9 (26 shillings, 9d) ; Quartiles, 24/2, 32. 
Deciles, 20, 23/6, 24/9, 25/8, 26/9, 28/2, 31, 33/4, 
35/4. 



230 DATA AND THEIR RELATIONS 

Mode, 25/3; secondary positions (modes), 16/6, 36. 

Curves may also be employed to show the relations 

between two or more sets of variable quantities. Thus : 



Marriage rate per 1000 
Imports and E)xports per head. 



Price of Wheat per quarter 



20 



tn 

(L> 

ca 

1^15 

o 

Sio 



o 

<u 5 

a 



00 







\ 



/\ 



• — ^"v 



./\ 



"^ \../--\...'-' 



q CO 

60^ J! 

1-1 



40^ 



V4 

o 

H-l 

o 
CO 



20^ 



1860 



1870 



1880 



1890 



^96 



Fig. 6. 



There are many opportunities for error in such a 
case as this. For example if the scale for the marriage 
rate were twice as great, the fluctuations in the curve 
would appear to be greater in comparison with those 



THE PROBABILITY CURVE 



231 



In the other curves. (See Bowley, loc, cit,) Great 
caution is necessary in the comparison of curves. 




The Probability Curve. — The curve represented by 
Fig. 7 is of great value in scientific investigations. It 
is sometimes known as the Probability Curve, or the 
Normal Curve of Error. Suppose a large number of 
measurements of a given quantity, or variations from 
a given standard; if no causes of constant error 
are present, errors of excess are equally probable with 
errors of the opposite sort as we have already seen 
(page 210) ; moreover large errors are less probable 
than small errors and very large errors are very improb- 
able. Let the line Mm represent the correct measure- 
ment ; let the part of the curve to the right of this line 
represent the positive errors (errors in excess), and the 
part to the left, those which are negative ; the size of an 



232 DATA AND THEIR RELATIONS 

error would be indicated by its distance from M along 
the base line. MF would indicate a small positive 
error ; MS^ a large negative one ; height above the base 
line indicates the comparative number of the errors ; 
thus the line Ff means a large number of small errors ; 
the line Ss, a small number of large ones. The curve 
may represent not only errors, but any series of quan- 
tities grouped about a type, when the causes of variation 
are very numerous and are independent of each other. 
In an earlier example it appeared that in tossing a coin 
the various possible series of runs of heads or tails 
could be stated in a series of figures which were related 
to each other as are the coefficients in the expansion 
of a binomial to the power indicated by the number of 
throws. 

This formula can be used in any case in which a 
number of independent variable factors is concerned. 
If the number is very large the chances of the various 
possible combinations can be represented by the curve 
we are discussing, as for example, in the case of the 
stature of adult males. Many factors enter into the 
determination of stature, such as heredity, health in 
childhood, kind and quality of food, occupation, and 
so on ; the statures of men in any given community are 
ranged on either side of the mode in such a way as to 
be represented with substantial accuracy by the proba- 
bility curve (or the Curve of Frequency or of Distri- 
bution, or the Normal Curve of Error, as it is vari- 
ously called). 

Let us suppose, however, that some constant factor 
is introduced tending to alter stature in a given direc- 
tion ; what effect will this have on the curve.? It will 



IRREGULAR CURVES 



233 



obviously change its form, for a greater number of 
cases will appear on one side of the former mode and a 
smaller number on the other; instead of being sym- 
metrical it will be skewed to one side or the other, thus : 




Fig. 8. 

The presence of a skew always indicates the opera- 
tion of some constant factor. If in tossing coins we 
found such a skew toward the side representing a large 
number of heads we should have evidence of the pres- 
ence of some constant factor favoring heads. 

Sometimes the representation of a series of quan- 
tities would produce a curve of still more irregular 
shape, such as this: 




Fig. 9. 



Such a curve would show that the group was not 
homogeneous ; that there was really a combination of 
two groups ; or that certain factors were operative in 
one part of the series and not in another. Professor 



234 



DATA AND THEIR RELATIONS 



1 



Thorndike^ gives the following curve as representative 
of the frequency of death at different ages, the age 




Fig. 10. 



increasing as we go from left to right. Certain factors 
are operative in early infancy that play no part later. 

1 In his Theory of Mental and Social Measurements, p. 51. See 
this book for discussion of measurement. 



I 



% 



PART III 
THE CONSTRUCTION OF SYSTEMS 



CHAPTER I 
EXPLANATION 

What is Explanation ?-Probability 5 classification and 
the discovery of laws all have to do with facts. 
Probability tells us the frequency with which a fact 
may be expected to occur; classification puts the fact 
into a group of like facts, and the better the classifica- 
tion from a scientific point of view, the more does the 
placing of the particular fact tell us with regard to 
its relations of resemblance and difference with other 
facts. A law states the conditions under which a fact 
occurs. In which of these cases can we be said to 
explain a fact.^^ 

The statement of the frequency with which an event 
occurs does not explain the event. We may say that 
the order of nature is such that, unless some change in 
the conditions is introduced, we may expect an event to 
occur with the same frequency in the future as it has 
manifested in the past ; but that is obviously very far 
from an adequate explanation. 

Do we explain an event when we classify it.^ When 
we ask why a given body fell to the ground, do we ex- 
plain the phenomenon by saying that it was a heavy 
body? Not entirely, and if we did not already know 
some law holding for heavy bodies, our statement would 
throw no light on the subject. It is quite true that a 
statement of this sort may be a preliminary to ex- 
planation. 

937 



238 EXPLANATION 

A law tells us how phenomena of a given sort be- 
have; it states the conditions of their occurrence, and 
if we can not say what sort of thing a given fact is we 
can not state its conditions. In bringing a fact under 
a law we first approach an explanation of it. Explana- 
tion has been defined as (in positive science) " the 
reduction of a phenomenon to the terms of a general 
principle, whatever that principle may b^." ^ 

Have we reached a final and complete explanation 
of a fact when we have brought it under a general prin- 
ciple.^ In many cases this seems to be sufficient; if 
we are familiar with the law and if we can see its bear- 
ing upon the fact in question, we are ordinarily content 
with this sort of explanation. An eclipse of the moon 
IS sufficiently explained for ordinary purposes if we 
are told that it is caused by the presence of an opaque 
object between it and the source of its light. Or the 
revolution of the moon about the earth may be ex- 
plained by saying that it is the resultant of the opera- 
tion of centripetal and centrifugal forces. 

But there are two further questions that may be 
asked. First, what are the circumstances in which the 
law operates in the present case? and second, how is the 
law itself to he accounted for? Let us consider the 
second question: How is a law to be explained? The 
answer is : By showing that the law is itself a case of 
a more general law. The attraction of the earth for 
bodies on its surface is explained by showing that it 
is a case under the law of gravitation. " It has often 
been found that scientific men were in possession of 

1 Dictionary of Philosophy, etc. Ed, Professor J. Mark Bald- 
win. 



SYSTEMATIZING DATA 239 

several well-known laws without perceiving the bond 
which connected them together. Men, for instance, had 
long known that all heavy bodies tended to fall towards 
the earth, and before the time of Newton it was known 
to Hooke, Huyghens and others, that some force prob- 
ably connected the earth with the sun and moon. It 
was Newton, however, who clearly brought these and 
many other facts under one general law, so that each 
fact or less general law throws light upon every 
other." ^ 

How far can this be carried? Do we not at last 
arrive at laws which are elementary and not to be ex- 
plained by reference to anything simpler or m.ore fun- 
damental? Are we then to regard these elementary 
laws as Inexplicable? No, for reference to simpler and 
more fundamental laws is merely one method of bring- 
ing the data into a system. If the elementary law can 
be shown to be a part of a system, made up, for example 
of other elementary laws, we have all the explanation 
which can be demanded. The parts are explained by 
being given their proper place In the whole. If the 
whole were In turn a part of a larger whole it could be 
explained In the same way. But suppose the whole 
were ultimate: could It be explained? Could the uni- 
verse, — not simply the physical universe, but the whole 
of reality of whatever kind, — could It be explained? 
The only kind of explanation which could be given 
would be a statement of the relation between this whole 
and Its parts, and It Is hard to see what other kind 
could be asked for. One might ask for the purpose of 
it all, but In the broad way In which we are conceiving 

2 Jevons, Lessons in Logic, p. 268, 



240 EXPLANATION 

of it, whatever purpose existed would be included in the 
whole itself.^ 

The explanation of a law (or fact) involves not 
merely showing that it is a case under a general rule, 
but also in discovering its relations to other laws and 
facts aside from the general rule under which it is 
brought. Along with other laws and facts it consti- 
tutes an interrelated whole, and explanation might 
better be defined as giving the thing to be explained 
its place in an organized system. We may wish to 
know not only the general law or laws under which the 
special case falls, but also the other special cases which 
are related to it ; or in other words, we may wish to 
know the general law and also the circumstances of its 
application in the present case. 

We can distinguish between explanation in general 
terms and specific explanation. The first consists in 
assigning the general law ; the second in showing, in 
addition to this, how the general law applies. The 
explanation of the moon's eclipse as given above is of 
the first sort ; if we should supplement it by stating 
that the intervening body is the earth and show how 
the earth and moon are situated with reference to the 
sun, we should have a nearer approach to a specific 
explanation. If we should go further and give an ac- 
count of the way in which they happened to be in these 
positions at this particular time we should have a still 
more complete and specific explanation. The explana- 
tion of a fact, to be absolutely complete and specific, 
would have to contain a statement of all the laws of 

^ See Hobhouse, The Theory of Knowledge, chapter on " Ex- 
planation." 



COMPLETE EXPLANATION 241 

the system to which the fact belonged and also a de- 
scription of all the facts contained in the system. Or 
otherwise expressed, a complete specific explanation 
would present all the facts which were related to the 
one to be explained, together with the laws under which 
each and every one of these relations fell, in a single 
unified whole. If an explanation is complete we can 
start with the laws and circumstances involved and 
show that the phenomenon to be explained would neces- 
sarily follow from them. Such an explanation might 
be possible in some parts of the field of astronomy ; if 
not an absolutely complete explanation, it could be suf- 
ficiently complete for all ordinary purposes. Complete 
grasp of a system would enable us to reconstruct the 
past or predict the future of the system. The astrono- 
mer's knowledge of the solar system is so thorough that, 
starting from the present position of any member of 
the solar system and knowing the relation in which it 
stands to each of the others, he is able to calculate the 
present position of any of the others and also to recon- 
struct their relative positions in the past or to predict 
their positions in the future; he can state the number 
and dates of eclipses which took place a thousand years 
ago and he can calculate the relations of any member of 
the system to any other at any given time. The only 
limits to such calculations are those which result from 
an imperfect knowledge of the solar system itself and 
ignorance of many possible disturbances from without. 
If a system were entirely isolated and if its laws were 
completely known, then a description of the system at 
any given time would make possible a description of it 
at any other time. Needless to say there is no system 



242 EXPLANATION 

of facts in nature which is entirely independent of the 
rest. Every system of facts is related to every other 
system, either directly or indirectly. To get a com- 
plete explanation of any single fact it would be neces- 
sary to know the whole system of nature. To a knowl- 
edge of all the laws of nature and all their relations 
to each other, it would be necessary to add a complete 
description of the relations of the parts of the system 
to each other. Then we could have an explanation of 
the fact which would show its relations to the whole 
and to every part of the whole. Obviously, an ex- 
planation of this sort can not be given for any fact. 
If it could be given for one it could be given for all. 
In this sense, Tennyson's lines are literally true: 



(( 



Flower in the crannied wall^ 

• • • • • 

If I could understand 
What you are^ root and all^ and all in all^ 
I should know what God and man is." 



Sometimes we are satisfied with an explanation in 
general terms, in terms of some familiar law. Some- 
times we call for an explanation of the law and are 
satisfied if it can be referred to some more general law 
or to some familiar system.^ 

4 Each of the " explanatory " sciences deals with some limited 
group of facts and attempts to discover the system of laws which 
holds within that field. Every one of the positive sciences takes 
for granted certain general principles, valid for all knowledge, and 
tries to discover a system of laws which shall be valid for its own 
field. A demand for the explanation of a physical fact, which is 
not satisfied with a statement of its relation to other physical 
facts in terms of physical laws, is not a problem for the science 
of physics. Ultimate explanations are for an ultimate science; 
philosophy is sometimes defined as this ultimate science. The 
laws which underly all the other sciences would be the province 



THE AIM OF MOST SCIENCES MS 

The aim of most of the sciences is not to explain par- 
ticular facts but to furnish the general laws, which may 
be employed in explanation of facts in a given field. A 
science like mechanics, for example, " lays down prop- 
ositions which are true in the same way of all fluids, all 
gases, etc., and represents them as general consequences 
of general presuppositions." " It does not descend 
into the whole manifold of the given, inasmuch as it 
deals only with events which take place in a similar 
manner in bodies differing in many other respects. 
That this or that phenomenon falls under these laws is 
a matter for subsumption in dealing with the particu- 
lar ; it is not necessary to the completeness of the ar- 
rangement as a whole. The mechanical theory of gases 
disregards their chemical diff^erences in so far as they 
do not aff^ect its special province by giving rise to dif- 
ferences of specific gravity ; it is no part of its task to 
enumerate how many sorts of gases there are: it is 
enough to say that if a body is a gas it conforms to 
certain laws of compressibility, of expansion by heat, 
or of capacity for heat, etc." ^ 

Corresponding statements might be made about any 
one of the sciences which aim at the discovery of laws 
(as distinguished from the classificatory sciences, which 
aim only at the complete classification of facts). 

of such a universal science. It would be related to the particular 
sciences as they are related to the concrete data which they in- 
vestigate. It would not be complete till each of them was com- 
plete, nor could any of them be final until it had reached its 
goal; just as, in any one of them, no fact is completely known 
unless the general body of laws is known, and the body of laws 
can not be completely known until every fact can be accounted 
for. Progress consists in alternate advancements toward com- 
pleteness along both lines, from both directions. 
5 See Sigwart, Logic, Part III, chap. vi. 



9A4< EXPLANATION 

Specific Explanation. — But in practical life and in 
the historical sciences we are concerned with the con- 
crete individual fact ; hence propositions which deal 
with general properties and the like are of no use to 
us unless we can see how they apply in the particular 
case; and usually we cannot see that unless we have 
independent knowledge of the attendant circumstances. 
The knowledge of the single fact and of the general 
law under which it falls does not ordinarily enable us 
to reconstruct the system ; our knowledge of both fact 
and laws is too incomplete to enable us to get a specific 
explanation ; and a general explanation is not sufficient 
as a guide for action. 

Suppose that the fact under investigation were a 
criminal act of some sort; the object of the prosecut- 
ing attorney is to fix the responsibility for the act. In 
order to do this it is necessary for him to reconstruct 
the circumstances surrounding the doing of the act. 
In other words, he must build up the system of con- 
crete facts to which the act belongs. A Sherlock 
Holmes might be able, by superior powers of observa- 
tion, unusual knowledge of the laws of criminal be- 
havior, and so on, and by extraordinary skill in bringing 
each fact observed under the proper law, to reconstruct 
the whole system of facts without reliance upon the 
testimony of others ; but ordinary mortals would usu- 
ally find it necessary to collect evidence from all pos- 
sible sources, and then, out of the scattered bits, to 
restore some semblance of the original whole. One 
fact, sufficiently described, and a thorough grasp of the 
principles of the system, might be enough ; lacking that, 



THE APPLICATION OF SCIENCE 245 

as many fragments as possible must be collected, and 
even then no certain result might be reached. 

Knowledge of the laws alone does not ordinarily 
suffice, and even if that knowledge were complete it 
might be possible to go astray in applying it. The 
greatest scientist might fail in the attempt to give a 
specific explanation of a concrete fact if he should over- 
look the circumstances surrounding the fact. Specific 
explanation is a matter for the application of science, 
and theory alone is proverbially insufficient as a guide 
for practice, no matter how correct the theory may be 
in the abstract. The " theorist " may have an incorrect 
theory or he may fail to note the special circumstances 
in applying one which is correct. 

Closely related to the processes of explanation are 
those of prediction. They are complementary. In 
explaining, we give the laws and circumstances which 
account for a fact or a supposed fact ; in prediction 
we set out from a set of laws and circumstances and 
attempt to show that a certain fact will occur in the 
future or will be found on further investigation to 
exist. Successful prediction is, as we have seen in 
studying the inductive methods, a test of the validity 
of the laws we are employing. If we do not know the 
laws and circumstances we can not predict successfully, 
except occasionally and b}^ accident. Prediction may 
be said to represent the practical application of 
science. 



CHAPTER II 
HYPOTHESIS 

What is an Hypothesis? — Before we go on to the 
discussion of certain typical systems, it is necessary to 
give some attention to another matter involved in most 
explanations, namely, the use of hypotheses. The 
term hypothesis is used in several different senses, but 
for our purposes an hypothesis is a provisional explan- 
ation. Fictions made for the purpose of argument, 
illustration, or simplification may also be regarded as 
hypotheses, but we shall use the term in the narrower 
sense/ 

Hypotheses, or provisional explanations, may assert 
the existence of a fact, as when we assume that a de- 
fective flue was the cause of a fire ; or of a law, as 
when we infer a causal connection between vaccination 
and freedom from smallpox; or of a complex system 
of laws and facts, as when we infer the existence of a 
matriarchal system in the early history of certain 
peoples. Inductive inferences, which were discussed in 
chapter vi., would fall under the head of hypotheses. 

The Value of Hypotheses. — There has been much 
disagreement regarding the value of hypotheses and 
their use in science. A good many scientists have de- 
clared that hypotheses are not only unnecessary but 

1 For an interesting discussion of the subject, see Muir- 
head, Philosophy and Life, Art. " Hypothesis." 

24>6 



_^*j 



OPPOSITION TO USE OF HYPOTHESES 247 

are positively harmful, and Newton's " Hypotheses 
non pngo " is often quoted in defense of their position. 
To apply this literally would mean that a science would 
remain merely a body of carefully observed and classi- 
fied facts, unless laws should somehow or other spring 
ready made from them without having been previously 
put forward as possible laws and then tested by further 
observation and experiment. Now, it might sometimes 
be possible to collect our facts over a very wide range 
and classify them and their relations in such a way 
as to show at once the law of their connections ; the 
inductive methods indicate the sort of grouping 
that would be necessary ; but even with their assistance 
it would rarely happen that a fully verified law would 
appear without previous unsuccessful attempts at its 
discovery. Previous to the Nineteenth Century the 
progress of science was seriously retarded by what 
Romanes has called the Bugbear of Speculation. In the 
introduction to his Darwin and after Darwin he 
gives the following statement of the situation in the 
natural sciences : " Fully awakened to the dangers of 
web-spinning from the ever fertile resources of their 
own inner consciousness, naturalists became more and 
more convinced that their science ought to consist in 
a mere observation of facts, or tabulation of phe- 
nomena without attempt at theorization upon their 
philosophical import. If the facts and phenomena pre- 
sented any such import, that was an affair of the man 
of letters to deal with ; but as men of science, it was 
their duty to avoid the seductive temptations of the 
world, the flesh and the devil, in the form of specula- 
tion, deduction, and generalization . . . this was the 



248 HYPOTHESIS 

orthodox and general view." It was current in the 
time of Linnaeus and even to the time of Cuvler. " The 
Origin of Species made an epoch . . . Darwin dis- 
played the true principle which ought to govern bio- 
logical research ... he never loses sight of the dis- 
tinction between fact and theory . . . but his Idea of 
the scientific use of facts Is plainly that of furnishing 
legitimate material for the construction of theories 
. . . the spirit of speculation Is the same as the spirit 
of science, namely, to know the causes of things . . . 
If It be causes or principles as distinguished from facts 
or phenomena, that constitute the final aim of scientific 
research, obviously the advancement of such research 
can be attained only by the framing of hypotheses. 
And to frame such hypotheses is to speculate.'' Dar- 
win said of himself that he made an hypothesis on every 
subject. " He was as productive of hypotheses as 
nature is of living things, and like her, he subjected 
them all to the principle of natural selection." ^ 

Hypotheses are necessary for science. " All science 
starts with hypotheses, In other words, with assump- 
tions that are unproved, while they may be and often 
are erroneous ; but which are better than nothing to 
the seeker after order In the maze of phenomena." ^ 

An erroneous hypothesis may be quite as effective 
in the field of practical activity as a true one could be. 
" The theory that some god would destroy the tribe If it 
did not wash at a particular time was a very crude ex- 
planation of an observed fact ; but it nevertheless has 
Its merits. It caused the tribe to wash occasionally — 

2 Cramer, The Method of Darwin, p. 40. 

3 Huxley, Hume, p. Q5, 



MISTAKEN HYPOTHESES 249 

a thing it would never have done. It furnished a 
theory which tended to prevent disease. It recognized 
the truth which bacteriological science has only just 
grown up to in the present generation: that the pen- 
alty for violation of law was visited not so much on 
the individual as on the community.^ 

The Ptolemaic System was an erroneous hypothesis, 
but without it, or some other theory, astronomical 
knowledge would have progressed much more slowly 
than it did. " The superiority of the Greeks to their 
Oriental neighbors in science has often been accounted 
for by their fertility In theory. The Oriental peoples 
were, at the time of which we write (Cosmological 
Period), considerably richer than the Greeks In accu- 
mulated facts, though these facts had certainly not 
been observed for any scientific purpose, and their pos- 
session never suggested a revision of the primitive view 
of the world.'' ^ 

The danger In using hypotheses lies In the fact that 
we are so likely to forget that they are only hypotheses. 
We find some explanation which seems to fit the facts 
or which supports some other belief of ours, and we 
forget that our hypothesis has not been verified. We 
tend to have too great a fondness for hypotheses which 
we have ourselves made ; we are liable to " the partiality 
of Intellectual parentage.'' Darwin's example may 
again be cited as the right one. " I have steadily en- 
deavored to keep my mind free so as to give up any 
hypothesis, however much beloved (and I cannot resist 

• 

4 President Hadley, in an article in the Atlantic Monthly, Feb- 
ruary, 1903, p. 153. 

5 Burnet, Early Greek Philosophy, 1st Ed., p. 22. 



250 HYPOTHESIS 

forming one on every subject), as soon as the facts 
are shown to be opposed to it. Indeed, I have had no 
choice but to act in this manner, for, with the exception 
of the Coral Reefs, I cannot remember a single first- 
formed hypothesis which had not after a short time 
to be given up or greatly modified." ^ 

It has been said that an hypothesis is a question.*^ 
When we form an hypothesis our attitude should be 
described by the inquiry : " Is this the true explanation 
of the facts .^ " If that attitude could be preserved the 
danger from hypotheses would be very small. We often 
hear of " working hypotheses." They are simply 
hypotheses which are confessedly unverified but valu- 
able as a basis on which to work toward an explanation. 
There may be many degrees of verification, from the 
most complete to the most imperfect ; strictly speak- 
ing, one might say that until an hypothesis has been 
proved true and show^n to be a law (and therefore no 
longer a mere hypothesis) it remains a working hypo- 
thesis ; but in ordinary usage this term is used to de- 
scribe hypotheses which are useful but in no sense 
established. 

One way of holding the mind open to the fact that a 
given hypothesis is not to be trusted too far would 
be to keep before us a number of diff'erent rival hypo- 
theses.® 

6 Life and Letters, Vol. I, p. 83, quoted in Cramer's Method of 
Darwin 

7 Langlois and Seignobos, Introduction to the Study of History, 

8 This method, which has been called the " Method of Multiple 
Working Hypotheses," has been recommended as promoting thor- 
oughness, suggesting lines of inquiry, as a means of sharpening 
discrimination, increasing fertility in reasoning processes, etc. 
See Chamberlain, The Method of Multiple Working Hypotheses, 
Science, Feb. 7, 1890. 



THE DERIVATION OF HYPOTHESES 251 

How are Hypotheses Suggested to Us? — We have 
already seen that the groupings of facts or sequences 
such as we use In applying the method of Agreement 
and the rest lead to the formation of inductive hypo- 
theses. Indeed (1) any sequence may do this. If we 
notice that A is followed by B, we tend naturally, in 
the absence of evidence to the contrary, to believe that 
the second will always follow the first. The statement 
that these two are universally and necessarily connected 
in this way is an hypothesis unless or until further ex- 
amination shows that the statement is either true or 
false. 

(2) Analogy. — A second ^ source of hypothesis is 
found in Analogy, The term analogy has been used in 
a good many different senses. ^^ In its broadest sense 
it means any kind of resemblance. An inference from 
analogy is inference from the resemblance of two cases 
in certain observed points to their resemblance in a fur- 
ther particular which has been observed in only one of 
them. For example, we may observe, in examining the 
skulls of certain extinct animals, that they all have 
sharp canine teeth and rudimentary molars ; in this 
respect they resemble modern carnivorous animals ; 
hence we infer that these extinct animals were carnivo- 
rous. Or we know that a boy who is ill has eaten unripe 
fruit; we infer that another boy who shows similar 
symptoms has been guilty of a similar indiscretion. 
Inference from analogy is usually to some particular 

9 A third source of hypotheses is found by Sigwart in the Con- 
version of propositions. For example, isosceles triangles have 
the angles at the base equal. Is the converse true? See Sig- 
wart, Logic, ii, p. 83. 

10 See Minto, Logic, p. 367. 



252 HYPOTHESIS 

fact or situation, though it may be further extended 
to a general principle. 

Analogy alone is notoriously an unsafe guide; but 
if certain general rules are kept in mind it may often 
be employed to advantage. 

1. If two sets of facts resembled each other in only 
one particular or in very few, an inference as to their 
resemblance in another particular would be very haz- 
ardous. The fact that two men were born in the same 
city gives no ground for the conclusion that one will 
have the same profession as the other. 

2. If two sets of facts resembled each other in every 
particular except such as were irrelevant, the inference 
would be safe. Reasoning by analogy in geometry 
illustrates this. Again, if two animals were alike except 
in color, the fact that one was carnivorous would be 
good ground for believing that the other was too. 

3. In so far as two things or two sets of facts dif- 
fered in relevant particulars the inference would be of 
doubtful value. If one of two twins had been educated 
in one way and the other in a different way, it would 
not be safe to infer that one would be interested in the 
things in which the other was interested. 

4. If one of two similar things possessed a char- 
acteristic inconsistent with a characteristic possessed 
by the other, it would of course be impossible to infer 
that the first thing possessed the latter characteristic. 
If A is a singer we cannot infer that his twin brother 
B is, if the latter is deaf and dumb. 

5. If the points of resemblance outnumbered the 
points of difference, we should have more reasons for 
than against the inference, provided, of course, that 



ANALOGY 253 

the various points were equally important in determin- 
ing" the character of the things in question. As a mat- 
ter of fact they never are of equal importance, so 
that the relative importance of the various character- 
istics should be taken into account ; a difference in 
health would count more against equal strength in two 
men than similarity of stature, weight and age would 
count in its favor. 

6. In counting resemblances and differences, only 
those which are independent should be counted; the 
fact that a planet possesses atmosphere and that it 
refracts light passing near its surface are not inde- 
pendent ; to count these as two points of likeness when 
trying to find ground for the conclusion that one 
planet resembled another in any particular respect 
would be incorrect. 

In practice it is not easy to say just what char- 
acteristics are relevant or to be sure whether two points 
are independent. -"^^ 

Analogy may be employed in connection with other 
grounds of inference ; for example, if a given situation 
possesses factors which are partly like and partly un- 
like those in another situation we might sometimes infer 
the presence in the second of some further character- 
istic possessed by the first, but in less degree. One 
man might exhibit some of the symptoms exhibited by 
another who was known to have taken a certain drug; 
we might infer that the first had taken a smaller quan- 
tity of the same drug, and so on. 

Requisites of a Good Hypothesis. — Having made 
our hypothesis on whatever ground, we should ask our- 
11 See Hobhouse, Theory of Knowledge, page 289, seq^. 



254 HYPOTHESIS 

selves whether it is worthy of serious consideration. 
To put the question in its usual form, What are the 
requisites of a good hypothesis? 

1. In the first place it must serve the purpose for 
which it is made ; it must offer an explanation for 
data which have not previously been explained cor- 
rectly. Sometimes certain other explanations may 
have been offered and found insufficient ; sometimes the 
data may have been entirely unexplained. An hypothe- 
sis which does not connect at least two facts hitherto 
not properly connected is worthless. 

2. A good hypothesis must, of course, be consistent 
with itself and with all the data concerned. It is some- 
times said that an hypothesis must not contradict known 
laws ; if there are laws which are completely verified, 
the hypothesis must be in agreement with them. 

That does not mean that an hypothesis must not 
disagree with any principles which have been hitherto 
accepted. Such reasoning would have ruled out the 
Copernican Hypothesis, and it did, as a matter of fact, 
lead many to reject that theory. Strictly speaking, 
any hypothesis which offers a consistent account of the 
data and their relations has a claim to consideration. 
In practical life we are often warranted in neglecting 
new theories which contravene accepted principles, at 
least until they have been shown to approach in value 
and soundness those already current ; but the specialist 
in any field is .not justified in rejecting a theory simply 
on the ground that it disagrees with those he has held 
in the past. It is his duty to test all of them. 

3. An hypothesis, to be worthy of consideration, 
must be capable of verification. If data for its verifi- 



REQUISITES OF HYPOTHESES 255 

cation are not already at hand they must at least be 
conceivable and their discovery must be within the 
bounds of possibility. Herodotus, in discussing the 
various theories of the rise of the Nile, says of the one 
which connected it with the mythical stream of Ocean: 
" The person who speaks about the Ocean, since he has 
transported the question to the dominion of the in- 
scrutable, does not admit of refutation." ^^ 

4. Other things being equal, choose the simplest 
hypothesis. 

Making hypotheses involves mental activities which 
go beyond perception and memory. They are often 
discussed under the heading of " Imagination." But 
imagination in this sense is not simply imagination in 
the limited sense of making mental pictures. It involves 
constructive activities often of a highly complicated 
sort. As " creative " imagination it differs from that 
of the poet in that it does not have to do necessarily 
nor primarily with concrete experiences.^^ 

EXERCISES. 

State the ground of the hypothesis in each of the follow- 
ing examples and estimate the value of the hypothesis: 

1. Geologists^ watching at what rate changes are occur- 
ring in the earth's surface at the present time^ — e, g., mak- 
ing of valleys^ glacier movements^ etc.^ — determine the 
length of time it must have taken to produce the corre- 
sponding changes during the so-called geological periods. 

2. In looking at the pictures in an art gallery^ our atten- 
tion is specially attracted by one picture whose character- 
istics impress themselves in our mind. Years afterward^ / 
in another country^ we again see those characteristics in ,J- 
another picture and we feel certain that both pictures are ^^ y 

the work of the same artist. HA^^"^^"^ *\/^^ 

12 Gomperz, Greek Thinkers, Bk. Ill, chap. p. 6. ^^ ^ - ^a 

13 Minto, i.O(/ic, pp. 335, 336, ^ ^ ^A^^"^^ 



256 HYPOTHESIS 

3. Cutting tools -have edges and places for handles. 
These flints have edges and places for handles; they are 
therefore^ cutting tools. 

4. Some Northwest Coast Indians after seeing and hear- 
ing a phonograph for the first time^ were asked what they 
thought it was. Their answer was that it was a very power- 
ful echo which the white man controlled by means of a 
** strong medicine '' or magic. 

5. The theory that many philologists hold^ that many of 
the languages of the world may be traced back to a common 
stocky known as the Aryan^ is based on analogy. In 
Persian^ Greek^ Sanscrit^ etc.^ several very simple words^ 
usually verbs^ such as to give and to be^, are found to have 
almost identically the same root^ from which resemblances 
the common descent is argued. 

6. Certain mountains^ which have large deposits of ba- 
salt, contain gold. When large deposits of basalt are found 
in other mountains, we may suppose that they also contain 
gold. If gold is not found, tin is. There seems to be a 
relation between deposits of basalt and deposits of gold. 

7. Noting that certain substances expand when they 
crystallize, and noting also that certain other substances 
expand when heated, I might infer that heat causes the lat- 
ter substance to crystallize and hence to expand. 

8. Since ether has been offered as the medium of trans- 
mission of light-waves, and since some forms of electricity 
are forms of wave-motion, we might say that ether is the 
medium of transmission of electricity. 

9. The U. S. is a republic and its citizens are prosperous 
and contented; we may therefore infer that if Cuba were a 
republic, her citizens would be prosperous and happy too. 

10. Hydrochloric acid turns blue litmus paper red; sul- 
phuric acid has similar properties, and we may infer that 
it, too, will turn blue litmus paper red. 

11. Bones resembling those of an elephant were found 
in a given locality. We conclude that, at some time or 
other, elephants lived in this locality. 

12. Cotton is grown in the U. S. in a moist, warm 
climate and a sandy soil; we may infer that Egypt, which 
has these characteristics, will also grow cotton. 



CHAPTER III 
TYPICAL SYSTEMS OF KNOWLEDGE 

An examination of the methods employed in estab- 
lishing certain typical varieties of systems of knowledge 
may help to make clearer the complexity of knowledge 
and the relations of the processes involved in getting 
it. Every system, as we have seen, contains laws. 
Some of them are systems of laws and general concepts ; 
others include also concrete facts. Let us take as an ex- 
ample of the first, the sort of system which is to be 
found in mathematics or mechanics ; and as examples 
of the second, the system of related facts which the 
historian or the criminal lawyer aims to establish. The 
other sciences lie between. 

We cannot, in our present discussion, begin at the 
very beginning. We must grant to the historian and 
the lawyer the generally accepted laws of human be- 
havior, the accepted principles of science, in short, the 
working materials of his science. To the mathema- 
tician, we must grant his concepts and axioms and 
postulates, and to both the general principles of scien- 
tific method. We wish merely to see how each employs 
these principles, what his method is. All these concepts 
and principles have been brought to hght in the course 
of human experience. The mathematician employs 
chiefly the processes of analysis and deductive reason- 
ing. Observation, testimony and, in general, the means 

257 



258 TYPICAL SYSTEMS OF KNOWLEDGE 

for knowing the concrete are, for the most part, left 
aside in his work. 

The Geometric System. — Let us take an example of 
scientific method as it appears in the science of geome- 
try. Other fields of mathematics differ from this in 
important respects, but for the purposes of illustra- 
tion geometry will be sufficiently representative. What 
is the starting point in geometry and what sort of sys- 
tem does it attempt to build? ^ Geometry starts, not 
with perceived objects as the natural sciences do, but 
with a set of concepts and propositions. Among its 
concepts are those of point, line, magnitude, equality, 
and so on. Some of these are definable in terms of the 
others, as " a point is that which has no magnitude." 
There remain, however, certain concepts which are inde- 
finable, viz,, those by means of which all the others are 
defined. Of these concepts there are two kinds : con- 
cepts of elements, and concepts of relations. Besides 
these concepts geometry has among its data certain 
propositions which express the relations which hold 
among its elements. These propositions are known as 
axioms and postulates.^ 

1 See Oswald Veblen, Popular Science Monthly, Vol. LXVIII, 
Art. "The Foundations of Geometry"; and Transactions of the 
American Mathematical Society, Vol. 5, No. 3, Art. " A System 
of Axioms for Geometry." 

2 No clear line of distinction was drawn by Euclid between 
axioms and postulates. Both were regarded as unproved and un- 
provable propositions which must be admitted as true by every 
one who understood them, as a priori truths. At the present day 
their a priori character is very widely questioned, but they are 
unprovable in that they can not be deduced from any simpler 
propositions. One way of distinguishing them was to define the 
axioms as common notions and the postulates as geometrical pre- 
mises which must be taken for granted. But the line was not 
clearly drawn and propositions which sometimes appeared as pos- 
tulates were at other times put among the axioms. 



MATHEMATICAL SYSTEMS 259 

As an axiom we may cite the first in the list: 
'^ Things which are equal to the same thing are equal 
to one another " ; and as a postulate : " A straight line 
may be drawn from any one point to any other point." 
" All right angles are equal to one another " has some- 
times been classed as an axiom and sometimes as a pos- 
tulate. Euclidian geometry may be defined as " a 
system of propositions codifying in a definite way our 
spatial judgments." Every one of its propositions 
can be deduced from its axioms and postulates, except- 
ing, of course, the axioms and postulates themselves. 
To prove any proposition we have simply to combine 
certain concepts and propositions into a coherent 
whole. 

Let us examine Proposition XV, Book I. " Where 
two straight lines (AB, CD) intersect each other, the 
vertically opposite angles made by them, are equal." 




The demonstration is as follows : " For the angle 
CFA + the angle AFD = two right angles (prop. 13), 
and also the angle AFD + the angle DFB = two right 
angles ; therefore the angle CFA -f the angle AFD = 
the angle AFD + the angle DBF (axiom 1) ; and the 
common angle AFD being taken away from both, there 
remains the angle CFA = the angle DBF (axiom 3) ; 
but these are vertically opposite angles. In like man- 
ner it may be proved that the vertically opposite angles 



260 TYPICAL SYSTEMS OF KNOWLEDGE 

AFD and BFC are equal." What are the concepts 
and propositions employed in the proof of this theorem? 
We have concepts of number (two, e. g.)^ straight 
lines, point, circle, intersection, angles, right angles, 
vertically opposite angles, equality, addition, subtrac- 
tion, remainder, etc. 

We employ, among the propositions. Proposition 
XIII (When a straight line standing upon another 
straight line makes angles with it they are either two 
right angles or together equal to two right angles) ; 
this proposition was proved from certain others all 
resting ultimately upon the axioms and postulates. We 
employ Postulate S (A circle may be described from 
any center, with any interval from that center) ; Postu- 
late 1 (A straight line may be drawn from any one 
point to any other point) ; Definition 12 (A circle is a 
plane figure bounded by one line called the circumfer- 
ence or periphery ; to which all straight lines drawn 
from a certain point within the figure, are equal) ; also 
Axiom 1 (Things which are equal to the same thing 
are equal to each other). 

Geometrical demonstrations are made with reference 
to figures, and it might seem as if we were really dealing 
with a concrete particular case instead of with general 
concepts alone ; but the concrete case is simply an 
illustration and the whole demonstration is absolutely 
general. Accurate measurements of the figure would 
undoubtedly show, inequalities between the vertically 
opposite angles for the reason that the lines are not 
absolutely straight ; the figure symbolizes the intersec- 
tion of any two absolutely straight lines and the dem- 
onstration is true of all such lines and only of such. 



PURE SCIENCES 261 

Similar statements apply to all the figures used in dem- 
onstrating geometrical propositions. Euclidian geom- 
etry as a whole is simply a complex system built up in 
the manner illustrated by the example above. 

The data of the geometrician are comparatively few 
and simple. His general principles are already deter- 
mined ; his tests of truth are agreement with his prin- 
ciples, and not absolute agreement with concrete facts ; 
however, he believes that if it were possible to observe 
and measure the facts accurately, and if facts could 
be found to agree with his definitions of straight line, 
circle, etc., for example, his conclusions would be found 
in correspondence with them.^ 

The system which we have just examined aims at the 
organization of a set of judgments having a general 
application and not with any specific data. The science 
of geometry is not interested in this or that geometrical 
figure ; it gives us information regarding figures of 
certain kinds, leaving the question of its application 
to particular cases to the applied sciences. All of the 
so-called " pure sciences " are like geometry in this re- 
spect. They deal with general principles, not with 
particular cases. Sometimes the arts and sciences are 
distinguished along this line, the arts being defined as 
the application in practice of the principles embodied 
in the sciences. The science of geometry is a system 
fouiided upon a certain few general principles which 
are described as axiomatic. 

Most of the sciences include, besides axiomatic prin- 

3 Recently, other systems of geometry have been built up. The 
methods employed are the same as those of EucHdian geometry, 
but they assume different postulates. The only requirement is 
that the system built upon them shall be a coherent whole. 



262 TYPICAL SYSTEMS OF KNOWLEDGE 

ciples, others which are the outcome of the apphcation 
of the methods of science to the study of empirical 
data. The science of Mechanics is an example of this. 
As we have seen, it " lays down propositions which are 
true in the same way of all fluids, all gases, etc." 
These laws were discovered as a result of a multitude 
of observations of the behavior of particular bodies of 
fluid, gas, etc. ; the observations were recorded, 
classified and made the basis of inductive inferences, 
which were tested as completely as possible. Hence 
all the processes included in the scientific method of es- 
tablishing laws are employed, but strong emphasis is 
placed upon the establishment of further conclusions 
on the basis of these laws, in other words, the deductive 
part of scientific method is emphasized. 

Somewhat similar statements may be made regarding 
the science of Chemistry^ though chemistry is perhaps 
less independent of particular facts and less able to 
proceed deductively on the basis of generalizations al- 
ready established; and certain departments of chem- 
istry are concerned rather with the classification of 
facts than with attempts to found a deductive science. 
Observation, analysis, classification and induction are 
all employed. Still, even In chemistry there is much 
that is deductive, and the interest of the chemist in 
particular facts tends to become only indirect. 

Biology and Psychology may also be mentioned at 
this point. Both are interested in concrete phenomena 
mainly for the sake of the general conclusions which 
may be based upon them. Both employ the whole of 
scientific method, including the use of statistics, aver- 
ages and probability. Both are farther than chemis- 



PSYCHOLOGY AND BIOLOGY 263 

try from the point at which a science begins to be 
primarily deductive. The employment of statistics 
and of methods of exact measurement has become of 
very great importance in these two sciences within the 
past few years. Reference to the recent literature of 
both subjects makes this very evident. As examples in 
psychology we might cite studies of animal behavior 
and studies in child psychology ; ^ in biology, the in- 
vestigations connected with Mendel's Law, the study 
of Variation, and so on.^ 

The pages from the works of Professor James (pages 
280-284), illustrate psychological analysis, which does 
not employ statistics ; and the essay from Huxley's 
works (pages 287-300) illustrates the same thing in 
the field of biology. Neither passage can be regarded 
as representative of the studies which are most fre- 
quent at the present time. Both are exceptionally 
broad in scope and deductive in character, but both 
do illustrate the desire of scientists in both fields to 
arrive at general conclusions and to establish coherent 
systems. 

Systems Which are More Concerned with Concrete 
Data. — We wish now to consider systems which have 
to do with concrete data in a different way ; systems 
which give to specific instances their exact place in a 
system of concrete facts ; systems w^hich not only pre- 
sent a body of general laws, but also apply them to the 
explanation of specific cases ; systems which state com- 
pletely the causes of given phenomena or enable us to 

4 See Yerkes, The Dancing Mouse; Washburn, The Animal 
Mind; Thorndike, Educational Psychology; and articles in jour- 
nals. 

5 See Punnett, Mendelism; and articles in journals. 



264 TYPICAL SYSTEMS OP KNOWLEDGE 

establish the existence of given events or situations 
not at present open to observation. 

History, in so far as it is concerned with the recon- 
struction of the past, is a case in point ; so also is the 
criminal lawyer's attempt to discover the individual 
guilty of a crime ; again Geology, when it aims at the 
discovery of past changes and conditions of the earth 
falls in the same class. In geology the primary data 
are almost entirely the present .character of the earth's 
surface and the changes which are constantly going 
on. It includes, of course, many of the data and con- 
clusions of physics, chemistry, and biology. On the 
basis of these data it is able to arrive at well-founded 
conclusions concerning changes which never could have 
been observed. It assumes, as does all science, that 
unless there is evidence to the contrary, the past and 
the unobserved are like the present and the observed. 

" Many of the changes which have indisputably taken 
place are such as no man has ever observed, because 
they are brought about so slowly or so deep down 
within the crust that no direct observation is pos- 
sible, and we can only infer the mode of procedure by 
examining the result. No human eye has ever witnessed 
the birth of a mountain range, or has seen the beds 
of solid rock folded and crumpled like so many sheets 
of paper, or observed the processes by which rock is 
changed in all its essential characteristics ; ' metamor- 
phosed ' as it is technically called." ^ Conclusions of 
this character imply the existence of a well organized 
body of knowledge concerning the relations of facts 
in the given field. 

6 Scott, Introduction to Geology, p. 30. 



ASTRONOMY 265 

The data of the science were obtained by observation ; 
the facts observed were classified and correlated ; laws 
were gradually discovered and verified ; systems were 
constructed and rejected until eventually a set of gen- 
eral principles emerged upon which geologists could 
agree; but the working out of the details and the ex- 
position of the system of concrete facts involved — 
in other words the history of the earth — has progressed 
only a little way. In geometry observation is only 
incidental ; in any concrete science it is a constant neces- 
sity. In a historical science the particular fact occu- 
pies the center of the field; in other sciences the pri- 
mary interest is in generalizations. 

The discovery of the planet Neptune implied the 
construction of a similar system in Astronomy, The 
planets move in elliptical orbits ; these orbits, how- 
ever, are not perfect ellipses ; there are variations (per- 
turbations) due to the influence of other planets. The 
amount of variation due to any planet can be calcu- 
lated. In the case of the planet Uranus, after all the 
perturbations due to the known planets had been taken 
into account, there remained a resiidue unaccounted for. 
Adams and Leverrier calculated that this residue could 
be accounted for by the hypothesis of another planet 
in a given direction and at a given distance from 
Uranus ; and this planet was soon after discovered with 
the aid of the telescope and was named Neptune. The 
discovery of Neptune presupposed a knowledge of the 
general laws of the solar system and a comprehensive 
description of the relation in which its known mem- 
bers stood to each other. It was the result of the ap- 
plication of the general laws to a concrete situation. 



266 TYPICAL SYSTEMS OF KNOWLEDGE 

Systems of Historical Facts. — Both astronomy and 
geology find a large part of the concrete data with 
which they deal open to observation ; geology to some 
extent and astronomy to a great extent depend upon 
the testimony of past observers. In the courts and in 
the investigations of the historian, testimony is of the 
first importance. We may then classify the data in 
these investigations as follows : 

1. Material facts. 

2. Testimony. 

Examples of material facts would be the articles 
found on the scene of the crime, etc., etc. ; and in 
historical inquiries, the ruins of buildings, roads, and 
other public works, tombs, ancient implements, works 
of art, etc., etc. The testimony may be either oral 
or written. Usually the historian must rely princi- 
pally upon written testimony. It is of many kinds, 
from the pictographs of primitive man to historical 
accounts like those of Thucydides and Tacitus. The 
problems of the historian are to collect the data, weigh 
the value of each of the items, and construct an account 
which will best organize the data into a coherent whole. 

A. His first duty will be to collect all the data pos- 
sible. The methods employed by the lawyer are suffi- 
ciently familiar in their general outlines. Details of 
his methods are beyond the scope of our discussion. 
We shall consider the procedure of the historian a 
little more closely. He must search for documents. 
" Documents are traces which have been left by the 
thoughts and actions of men of former times, '^ ^ whether 

7 Langlois and Seignobos, Introduction to the Study of History, 
This is a most valuable introduction to the method of history and 
should be read by everj student of scientific method. 



HISTORY 267 

material facts, such as works of art and the like, or 
written records. Some historians have described events 
so recent that It w^as possible to obtain the testimony 
of eye-witnesses. They were thus able to obtain a 
quantity of testimony not available for the later writer 
and to cross-examine their witnesses. Usually the dis- 
covery of documents has meant a search in all sorts of 
places for the testimony of contemporaries ; the ex- 
peditions and excavations carried on by the archaeolo- 
gists have as their object the discovery of such records. 
Archives, state papers, early histories, memoirs, in- 
scriptions, etc., furnish the chief sources. The problem 
grows easier with the growth of collections and li- 
braries. But new documents are constantly being 
found, and no one can say when the data have all been 
discovered. 

B. After the collection of the data comes the esti- 
mation of the value of its various items. Estimating 
the value of testimony is a special problem and we 
shall treat of it first.^ The problem is to discover 
what facts the documents establish. The questions to 
be raised are such as these : Who did such and such an 
act.? Who wrote such and such a poem.? Who founded 
Rome.? The answer involves the establishment of a 
system of facts and inferences justifying some one 
conclusion to the exclusion of all others. The establish- 
ment of such a system means the discovery of facts, 
their classification, the construction of hypotheses, and 

8 Estimating the value of testimony is so important a matter 
in inquiries of the sort we are now considering that the questions 
involved will be discussed somewhat more fully than in the intro- 
ductory chapter. All the machinery of scientific method may be 
needed to enable the historian to decide whether or not a record 
is trustworthy. 



268 TYPICAL SYSTEMS OF KNOWLEDGE 

the verification of these, and the organization of facts 
and generalizations into a system. We know facts by 
observation, by memory aided by inference, by infer- 
ence from the testimony of others, by inference from 
remains of former human activities, and from all sorts 
of natural events, and natural processes ; we group the 
data with reference to their bearing on various parts 
of the problem ; we use the inferences based upon past 
experience and formulate new ones ; we test our con- 
structions by all known means. 

Sometimes observations of natural phenomena may 
make up most of the data. Observations made by others 
may sometimes be easily verified. Experiments may 
be repeated ; the problem of getting correct descrip- 
tions of the facts may frequently be comparatively 
easy. But the sort of case which illustrates the estab- 
lishment of a system of concrete facts in all its com- 
plexity is that in which human testimony, as well as all 
other kinds of data is employed to determine the 
existence and character of some fact. Let us examine 
in outline the processes involved in guarding against 
error in the use of testimony. A number of pre- 
liminary questions must be raised: 

(1) The first of them is this: What is the testimony? 
What does the witness say? What is the content of 
the document. The testimony is the starting point. 
We must know what the words mean, what they pur- 
port to tell, what facts they are intended to represent. 
{a) In the case of the witness on the stand this ques- 
tion, though all-important, is usually comparatively 
easy of solution. In case of doubt he can be called 
upon for further statements, which will make plain his 
meaning. When he speaks in a foreign language there 



HISTORY 269 

is more difficulty, but !n any ordinar}^ description of 
facts, the difficulty is not great, (b) In the case of 
historical documents the difficulty may be insurmount- 
able. For centuries hieroglyphics could not be inter- 
preted at all ; and translations from ancient documents 
are always attended with danger. The difficulty of find- 
ing in one language exact equivalents of the words of 
another needs no emphasis. In such a case the most 
thoroughgoing comparison of the two languages may 
be necessary in order to determine the meaning of a 
document. Whole sciences, such as epigraphy or palae- 
ography, are devoted to the interpretation of ancient 
writings. 

(2) If the meaning of the statements contained in 
the testimony has been made clear, the next question 
is, of course: Are the statements true? And in order 
to answer this we may ask next; (a) Who made the 
statements, and is he qualified by knowledge, honesty 
and accuracy sufficient to enable us to rely upon what 
he says.? In the law courts, the identity of the witness 
is the first thing to be determined and made a matter 
of record. When the witness is before us the question 
of his identity is usually very easy to answer, though 
there are, of course, numerous cases in which error and 
deception might occur. And in the case of the pris- 
oner, the determination of identity is often an ex- 
tremely difficult matter, involving testimony and many 
other kinds of evidence. 

In the case of written documents the determination 

of authorship is one of the most difficult problems which 

the historian has to solve. ^ The name upon the title 

page of a book is, by itself, not conclusive as evidence 

» See Langlois and Seignobos, Bgok II, chap, ill. 



270 TYPICAL SYSTEMS OF KNOWLEDGE 

of authorship. In modern books the indications of 
authorship are usually fully given and are ordinarily 
reliable; fraud is possible, but is usually easily de- 
tected, though forgeries in the name of dead authors 
may be successful. But in the case of early books, and 
above all in the case of manuscripts, the difficulties are 
very great ; in the first place there may be no formal 
indications of authorship; or the work is perhaps 
ascribed to such and such a person. Was he the author? 

We should ask first: Did such a person ever exist .^^ 
To answer this, only the testimony of contempo- 
raries would be conclusive. In many cases it is not 
necessary to pause over this question, for there may be 
no doubt about the existence of the author ; but in case 
there should be, the testimony to his having existed 
must be tested like any other such evidence. Con- 
sistency of testimony and corroboration of one piece 
of testimony by another are necessary here as else- 
where. One of the best known examples of this problem 
is that of the existence of Homer. Absence of testi- 
mony in this and other cases is usually a presumption 
against the truth of what is alleged. 

Granted that there was such a person as the author, 
did he write the document before us.^^ What evidence 
is there of the genuineness of the document.? The 
evidence is of two kinds, internal and external. In 
examining internal' evidence, the question is: Is 
the document such as the alleged author could or 
would have written? Is the handwriting of a sort that 
was employed during the lifetime and in the country, 
etc., of the supposed author? If the document is in 
handwriting of the Eleventh or the Thirteenth Century, 



INTERNAL AND EXTERNAL EVIDENCE 271 

it was not written by an author of the Twelfth Century. 
And with regard to the style and forms of expression 
the same question may be raised. In legal documents 
this is a valuable test, for legal phraseology is very 
definite. Modern words or phrases in a supposed an- 
cient writing are, of course, conclusive against any 
argument for its genuineness. 

Mention of facts and allusions to events of every 
sort are most valuable in this connection ; and lastly, 
the opinions expressed or implied an the document are 
of great assistance in determining its genuineness, for 
some opinions could not possibly have been held at the 
time the document purports to have been written. Ex-- 
ternal evidence is to be found in references to the 
document, quotations, etc., by contemporaries or by 
those of later periods. 

Another complication is often present to add to the 
difficulty of determining authorship ; the document may 
be the work of two or more individuals, or changes may 
have been introduced by those who have edited the 
texts, or there may have been mistakes in copying. 
In all these cases one should not necessarily reject the 
work as a whole ; it may give some information and we 
may be able to detect the changes from the original, 
and it may be of great importance to determine just 
what was done by the original author or just what was 
written by each of several collaborators. The methods 
to be employed are of course those described above. 
It is simply a question of several authors instead of 
one. 

(b) Having assured ourselves of the identity of the 
witness or witnesses, the next question is: Was he in a 



272 TYPICAL SYSTEMS OF KNOWLEDGE 

position to know the facts to which he is testifying? 
Does he assert that he witnessed them himself? ^^ And 
was it humanly possible for any one to have observed 
the facts in question? And if this question can be an- 
swered in the affirmative, we have next to ask whether 
there is any reason why the witness himself could not 
have observed them. Was he (^) competent to observe 
and remember the facts? Was there any defect in his 
powers of observation, or is there any evidence against 
his having been at a place where the observation could 
have been made? Here again, when we have the wit- 
ness before us, the difficulty of solving the problem is 
much easier than when we have to rely upon written 
testimony, or other evidence of an indirect sort. 

Cross-examination is a method of getting at once an 
addition to the testimony on the points already raised 
and of furnishing immediately statements which will 
corroborate or disagree with statements already made, 
or with known facts. In Lincoln's first murder trial, 
the chief witness had testified to seeing the murder 
committed by the prisoner. In the cross-examination 
he added a number of details : that the shooting was at 
ten o'clock at night, in beech timber, in August, that 
he was twenty feet or more away, that he could see the 
pistol and how it hung ; that the nearest lights were 
half a mile away, and that he saw it all by moonlight. 
Lincoln showed that the moon did not rise till one 
o'clock in the morning. Cross-examination may bring 
out inconsistencies due to dishonesty as well as incom- 
petence, as shown in this example. Where cross-ex- 

10 As Bain asserts {Logic, Appendix I), "The supreme canon 
of historical evidence is testimony of a contemporary " — of one 
who may have observed the fact. 



TESTIMONY 273 

ammation is impossible, as in written testimony, it may 
be impossible to convict a dishonest witness. 

(ii) If the witness has withstood all the preceding 
tests we have next to ask whether there is anything in 
his record which would lead us to doubt his honesty or 
whether he is likely to have any reason for falsifying in 
the present case. The two questions are distinct ; a 
general good reputation would be a presumption in 
favor of his honesty in the present case, but it would 
not make it certain that he was proof against all temp- 
tation. In the courts, cross-examination of the wit- 
ness himself and the testimony of other witnesses fur- 
nish the data for answering the question; in written 
testimony, other statements of his own and the state- 
ments of his contemporaries must be taken into ac- 
count ; what is implied is often more important than 
what is stated outright. 

There are two cases in which the testimony of a wit- 
ness may be regarded as particularly free from wilful 
falsification. The first is that in which the witness be- 
lieves the evidence is to his discredit or disadvantage. 
One exception must be made: the witness, for the 
sake of satisfying a grudge or shielding someone else, 
might be willing to sacrifice his own reputation and 
advantage. In any case, such testimony would need 
further corroboration, but it would, with the excep- 
tion above mentioned, be excellent evidence of the good 
faith of the witness. 

The second case is that in which evidence is given 
undesignedly. The witness makes statements of whose 
import he is unaware or he is surprised into statements 
which bring out facts which he has been attempting to 



£74 TYPICAL SYSTEMS OF KNOWLEDGE 

conceal. An incident related in Voltaire's " Zadig " 
will illustrate this : 



Zadig's master^ Setoc^ had lent money in the presence 
of two witnesses who had died before the debt was paid. 
The debtor denied having received any money. The money 
had been counted out upon a stone near Mount Horeb. 
Zadig undertook to conduct the case. He summoned the 
debtor before a tribunal and demanded that the five hun- 
dred ounces of silver be returned to his master. *' Have you 
witnesses.^ " asked the judge. *' No/' replied Zadig^ *' they 
are dead; but there is a large stone on which the money 
was counted out; if it please Your Highness to order that 
the stone be sought out^ I hope that it will bear witness; 
the debtor and I will remain here until the stone arrives; 
I will have it hunted up at the expense of my master.'' 
** Very well/' replied the judge^ and he turned his atten- 
tion to something else. At the end of the sitting he said 
to Zadig^ '* Well^ your stone has not yet arrived.^" The 
debtor laughed and said: 'Hi your Highness should re- 
main here till to-morrow the stone would not have arrived; 
it is more than six miles away and it would require fifteen 
men to move it." ** Well/' cried Zadig^ " I told you that 
the stone would bear witness; since this man knows where 
it is^ he admits that it was upon it that the money was 
counted out." — Voltaire_, Zadig, Chap. x. 

Testimony which is false is of course evidence of 
something, — of the opinion of the witness, or of his 
character, or of the existence of certain ideas, etc., at 
the time in which he lived. 

But all these questions are more or less preliminary. 
A witness of good reputation and a good observer, 
with no motive to falsify, may, of course, be mistaken 
in the case under examination. And a witness who is 
not usually reliable or who is a bad observer or one with 
every reason to falsify, may be telling the truth. In the 



TESTIMONY 275 

first case the presumption would of course be in favor 
of the testimony and in the second against it, but in 
neither case could we regard the reliability of the testi- 
mony as settled. There are three conditions to the ac- 
ceptance of every piece of testimony, (1) It must bq 
self-consistent and internally coherent; (2) it must be 
consistent and coherent with other known facts re- 
lating to the same case; (3) it must be consistent with 
ordinary experience. 

1. If a witness, in one part of his testimony, makes 
a statement inconsistent with what he has stated pre- 
viously, his testimony is discredited. One of his state- 
ments may be true or both may be false ; it may be 
possible to show that one of them is consistent with the 
rest of his testimony, while the other is not, but the 
disagreement of these statements would tend to throw 
doubt upon the others, and without external corrobora- 
tion his whole story would be open to question. More- 
over, his statements, to have the greatest force, must 
not only be consistent, they must be coherent ; they must 
describe a connected series of events. If a lawyer can 
by cross-examination show that the witness has made 
inconsistent statements, the force of his testimony is 
often entirely destroyed; and it is usually very much 
weakened, at the very least. 

But even the most coherent body of testimony would, 
by itself, be insufficient to prove the existence of the 
facts alleged. Otherwise we should be obliged to ac- 
cept as true many acknowledged fictions. Indeed, too 
great coherence, too good a story, rouses the suspicion 
that it has been manufactured or at least modified, since 
most men are too inaccurate both in observing and in 



276 TYPICAL SYSTEMS OF KNOWLEDGE 

remembering to describe any complex set of events 
without minor inconsistencies. 

By itself, then, internal evidence is not conclusive; 
without the support of other testimony or of facts 
otherwise known any piece of testimony must be held 
as doubtful. A possible exception might be noted: 
if the testimony were of such a character that its falsity 
would be more difficult to understand and explain than 
its truth, we should have some ground for accepting 
it even in the absence of other corroboration ; but such 
cases would obviously be rare. 

Negative Evidence, — The absence of testimony to 
the existence of a fact which could hardly have failed 
of mention by contemporaries is a strong presumption 
against its existence. If an alleged work, or doctrine, 
or what not, is referred to by no contemporary and is 
first mentioned by some later writer, it is probably 
false. The tradition regarding individuals, cities, and 
so on, often becomes more extensive and circumstantial 
as the objects of the tradition get farther away/^ 

2. In oral testimony, one of the most frequent sources 
of corroboration is to be found in the testimony of 
other witnesses. But too close an agreement, instead of 
being evidence of the truth of the testimony, raises a 
suspicion that the witnesses are in collusion and that 
the whole story may be false. The inevitable inaccu- 
racies of observation and of memory render it prac- 
tically impossible that two witnesses should tell stories 
that should agree in all particulars ; some diflPerences 
are to be expected, and sometimes there are diff'erences 
regarding some of the most important points. In writ- 

11 For illustrations, see Hayward, Essays, "The Pearls and 
Mock Pearls of History." 



TESTIMONY 277 

ten testimony, if there are several documents very 
closely similar, the presumption is that, instead of being 
independent pieces of testimony, they are all derived 
from the same source. This presumption is particu- 
larly strong if the errors happen to be the same in 
all ; if, for example, the same words are misspelled or the 
same misstatements of fact are made in all, this is 
good evidence that one of the documents was the source 
of the rest or that all were derived from some common 
source. Of course disagreement does not prove the 
truth of any one of the bodies of testimony, but it is 
good evidence of their independent origin. Where the 
truth lies must be discovered by further comparison 
and construction. 

3. The third test mentioned above was agreement 
with ordinary experience. What is known as the Argu- 
ment to Antecedent Probability would be included here. 
We ask : Is the alleged event one that would have been 
probable in the circumstances? Is it consistent with 
the known laws of nature and their familiar modes of 
operation? This test might, in practice, be applied 
first ; if, for example, testimony contained statements 
violating all ordinary experience or well-tested laws of 
nature, we might decline to go to the trouble of ap- 
plying the other tests. But this test is not necessarily 
final, for statements which disagree with our past ex- 
perience are very frequently found to be true and it has 
more than once happened that a supposed law of na- 
ture has been stated too broadly and has needed quali- 
fication. A too ready rejection of unusual statements 
is no more justified by a sound method than is a too 
ready credulity. But if the application of other tests 
leaves the truth of the testimony inconclusive, a viola- 



278 TYPICAL SYSTEMS OF KNOWLEDGE 

tion of ordinary experience would warrant the rejection 
of the testimony. If alleged facts were In contradic- 
tion to supposed laws of Nature, their existence could 
be established only by evidence which was stronger than 
the whole body of evidence in favor of the supposed law. 
Proof of the violation of all the laws of Nature would 
be impossible; for all proof requires the use of some 
law. We are often over-hasty in concluding that a 
statement is inconsistent with another or with some of 
the consequences of the latter, and we tend too readily 
to condemn anything which is apparently inconsistent 
with established principles. Rejection of the Coper- 
nican Hypothesis on the ground of its inconsistency 
with the principles of religion was a case of this sort. 

There are two or three topics which call for a little 
further discussion at this point. One of these is what 
is known as hearsay evidence; in this the witness re- 
ports not what he himself observed, but what he has 
heard some one else describe. Its value is very much 
less than is that of testimony to the fact itself. To the 
errors of the original observer, the errors of observa- 
tion, of memory, of description, and possible bad faith 
on the part of the original observer, we have added 
those of a second person, who is liable to the same errors 
and defects with regard to the words of the first. 

Tradition is simply hearsay evidence with a multi- 
plication of the number of intermediates between the 
last hearer and the original observer, if indeed, there 
were any observations at the beginning. It is evident 
that tradition is exceedingly poor evidence of the ex- 
istence of any fact. 



COMPLETE SYSTEMS 279 

Circumstantial evidence is merely indirect evidence : 
there may be no witnesses who have observed the facts 
themselves, but certain other facts may be incapable of 
explanation on any theory other than the one which 
asserts the existence of these facts. 

We have been discussing the problems of discovering 
and evaluating historical facts ; the principles involved 
in building up a system when the data are derived from 
both testimony and observation are, of course, the same 
as those involved in constructing a system from data 
obtained in any other way. We wish to get a complete, 
coherent whole. The framework of general statements 
or laws, and the particular structure which we build, 
must provide a place for the facts which are the ma- 
terials to be built into a system. If there are facts 
which do not fit, if there are parts of the framework 
which interfere with each other, if the laws of such 
structures are violated, the construction can not be 
accepted. A place for every fact, and a complete struc- 
ture when all the facts are in place, are the require- 
ments of a scientific structure, or, in other words, of 
any structure of knowledge which is to satisfy the de- 
mands of a reasonable being. 

The details of historical construction are beyond the 
scope of this outline and an illustration which should 
show them with any degree of fullness would occupy 
too much space. Huxley's argument, quoted on pages 
287-300), illustrates a few of the points. The student 
is referred to Langlois and Seignobos's Introduction to 
the Study of History for further discussion and illus- 
tration. 



280 TYPICAL SYSTEMS OF KNOWLEDGE 



EXERCISES 

In the following examples^ outline the argument and 
state the general principles employed^ and the way in 
which these principles were or might have been estab- 
lished; examine each step in the reasoning and determine 
whether or not it is valid; where inductive inference is 
used describe its foundation, and criticise, if possible; 
where the argument is incomplete state what would be 
necessary in order to complete it: 

I. Professor James's argument for his theory of the 
emotions, as given in his Psychology, Briefer 
Course^ pp. 375 to 380. 

** The feeling, in the coarser emotions, results from the 
bodily expression. Our natural way of thinking about the 
coarser emotions is that the mental perception of some 
fact excites the mental affection called the emotion, and 
that the latter state of mind gives rise to the bodily ex- 
pression. My theory, on the contrary, is that the bodily 
changes follow directly the perception of the exciting fact, 
and that our feeling of the same changes as they occur IS 
the emotion. Common sense says, we lose our fortune, are 
sorry and weep; we meet a bear, are frightened and run; 
we are insulted by a rival, are angry and strike. The 
hypothesis here to be defended says that this order of 
sequence is incorrect, that the one mental state is not imme- 
diately induced by the other, that the bodily manifestations 
must first be interposed between, and that the more rational 
statement is that we feel sorry because we cry, angry be- 
cause we , strike, afraid because we tremble, and not that 
we cry, strike, or tremble because we are sorry, angry, or 
fearful, as the case may be. Without the bodily states 
following on the perception, the latter would be purely 
cognitive in form, pale, colorless, destitute of emotional 
warmth. We might then see the bear and judge it best to 
run, receive the insult and deem it right to strike, but we 
should not feel afraid or angry. 

" Stated in this crude way, the hypothesis is pretty sure 



1 



JAMES' THEORY OF EMOTION 281 

to meet with immediate disbelief. And yet neither many 
nor far-fetched considerations are required to mitigate its 
paradoxical character^ and possibly to produce conviction 
of its truth. 

" 1. To begin with^ particular perceptions certainly do 
produce widespread bodily effects by a sort of immediate 
physical influence, antecedent to the arousal of an emotion 
or emotional idea. In listening to poetry^ drama^ or heroic 
narrative^ we are often surprised at the cutaneous shiver 
which like a sudden wave flows over us^ and at the heart- 
swelling and lachrymal effusion that unexpectedly catch 
us at intervals. In hearing music the same is even more 
strikingly true. If we abruptly see a dark moving form 
in the woods^ our heart stops beatings and we catch our 
breath instantly and before any articulate idea of danger 
can arise. If our friend goes near to the edge of a preci- 
pice^ we get the well-known feeling of * all-overishness/ 
and we shrink back^ although we positively know him to be 
safe^ and have no distinct imagination of his fall. The 
writer well remembers his astonishment^ when a boy of 
seven or eighty at fainting when a horse was bled. * The 
blood was in a bucket^ with a stick in it, and, if memory 
does not deceive him, he stirred it round and saw it drip 
from the stick with no feeling save that of childish curios- 
ity. Suddenly the world grew black before his eyes, his 
ears began to buzz, and he knew no more. He had never 
heard of the sight of blood producing faintness or sickness, 
and he had so little repugnance to it, and so little appre- 
hension of any other sort of danger from it, that even at 
that tender age, as he well remembers, he could not help 
wondering how the mere physical presence of a pailful of 
crimson fluid could occasion in him such formidable bodily 
effects. 

*' 2. The best proof that the immediate cause of emotion 
is a physical effect on the nerves is furnished by those 
pathological cases in which the emotion is objectless. One 
of the chief merits, in fact, of the view which I propose, 
seems to be that we can so easily formulate by its means 
pathological cases and normal cases under a common 
scheme. In every asylum we find examples of absolutely 
unmotived fear, anger, melancholy, or conceit; and others 



282 TYPICAL SYSTEMS OE KNOWLEDGE 

, of an equally unmotived apathy which persists in spite of 
the best outward reasons why it should give way. In the 
former cases we must suppose the nervous machinery to be 
so * labile ' in some one emotional direction that almost any 
stimulus (however inappropriate) causes it to upset in that 
way^ and to engender the particular complex of feelings of 
which the psychic body of the emotion corresponds. Thus^ 
to take one special instance^ if inability to draw a deep 
breath, fluttering of the heart, and that peculiar gastric 
change felt as * precordial anxiety/ with an irresistible 
tendency to take a somewhat crouching attitude and to sit 
still, with perhaps other visceral processes not now known, 
all spontaneously occur together in a certain person, his 
feeling of the combination is the emotion of dread, and he 
is the victim of what is known as morbid fear. A friend 
who has occasional attacks of this most distressing of all 
maladies tells me that in his case the whole drama seems 
to center about the region of the heart and respiratory 
apparatus, that his main effort during the attacks is to get 
control of his inspirations and to slow his heart, and that 
the moment he attains to breathing deeply and holding him- 
self erect, the dread, ipso facto, seems to depart. 

" The emotion here is nothing but the feeling of a bodily 
state, and it has a purely bodily cause. 

" 3. The next thing to be noticed is this, that every one 
of the bodily changes, whatsoever it be, is FELT, acutely 
or obscurely, the moment it occurs. If the reader has never 
paid attention to this matter he will be both interested and 
astonished to learn how many diiferent bodily feelings he 
can detect in himself as characteristic of his various emo- 
tional moods. It would be perhaps too much to expect of 
him to arrest the tide of any strong gust of passion for the 
sake of any such curious analysis as this ; but he can observe 
more tranquil states, and that may be assumed to be true 
of the greatest which is shown to be true of the less. Our 
whole cubic capacity is sensibly alive; and each morsel of 
it contributes its pulsations of feeling, dim or sharp, 
pleasant, painful, or dubious, to that sense of personality 
that every one of us unfailingly carries with him. It is 
surprising what little items give accent to these complexes 
of sensibility. When worried by any slight trouble, one 



JAMES' THEORY OF EMOTION 283 

may find that the focus of one's bodily consciousness is the 
contraction^ often quite inconsiderable^ of the eyes anr* 
brows^ When momentarily embarrassed, it is something in 
the 'pharynx that compels either a swallowing, a clearing 
of the throat, or a slight cough; and so on for as many 
more instances as might be named. The various permuta- 
tions of which these organic changes are susceptible make 
it abstractly possible that no shade of emotion should be 
without a bodily reverberation as unique, when taken in its 
totality, as is the mental mood itself. The immense num- 
ber of parts modified is what makes it so difficult for us to 
reproduce in cold blood the total and integral expression of 
any one emotion. We may catch the trick with the vol- 
untary muscles, but fail with the skin, glands, heart, and 
other viscera. Just as an artificially imitated sneeze lacks 
something of the reality, so the attempt to imitate grief 
or enthusiasm in the absence of its normal instigating cause 
is apt to be rather * hollow.' 

" 4. I now proceed to the vital point of my whole theory, 
which is this: If we fancy some strong emotion, and then 
try to abstract from our consciousness of it all the feelings 
of its bodily symptoms^ we find we have nothing left behind, 
no ' mind stuff ' out of which the emotion can be con- 
stituted, and that a cold and neutral state of intellectual 
perception is all that remains. It is true that, although 
most people, when asked, say that their introspection verifies 
this statement, some persist in saying that theirs does not. 
Many of them cannot be made to understand the question. 
When you beg them to imagine away every feeling of laugh- 
ter and of the tendency to laugh from their conscious- 
ness of the ludicrousness of the object, and then to tell 
you what the feeling of its ludicrousness is like, whether 
it be anything more than the perception that the object 
belongs to the class ' funny,' they persist in replying that 
the thing is a physical impossibility, and they always must 
laugh if they see a funny object. Of course the task pro- 
posed is not the impossible one of seeing a ludicrous obj ect 
and annihilating one's tendency to laugh. Tt is the purely 
speculative one of subtracting certain elements of feeling 
from an emotional state supposed to exist in its fullness, 
and saying what the residual elements are. I cannot help 



284 TYPICAL SYSTEMS OF KNOWLEDGE 

thinking that all who rightly apprehend this problem will 
agree with the proposition above laid down. What kind of 
an emotion of fear would be left if the feeling neither of 
quickened heart-beats nor of shallow breathings neither 
of trembling lips nor of weakened limbs^ neither of goose- 
flesh nor of visceral stirrings^ were present^ it is quite im- 
possible for me to think. Can one fancy the state of rage 
and picture no ebullition in the chesty no flushing of the 
face^ no dilatation of the nostrils^ no clenching of the teeth^ 
no impulse to vigorous action^ but in their stead limp mus- 
cles^ calm breathings and a placid face? The present 
writer^ for one^ certainly cannot. The rage is as com- 
pletely evaporated as the sensation of its so-called mani- 
festationSs and the only thing that can possibly be sup- 
posed to take its place is some cold-blooded and dispas- 
sionate judicial sentence^ confined entirely to the intellec- 
tual realm^ to the effect that a certain person or persons 
merit chastisement for their sins. In like manner of grief: 
what would it be without its tears^ its sobs^ its suffocation 
of the hearts its pang in the breast bone? A feelingless 
cognition that certain circumstances are deplorable and 
nothing more. Every passion in turn tells the same story. 
A disembodied human emotion is a sheer nonentitv. I do 
not say that it is a contradiction in the nature of things, 
or that pure spirits are necessarily condemned to colds 
intellectual lives ; but I say that for us emotion disassociated 
from all bodily feeling is inconceivable. The more closely 
I scrutinize my stateSs the more persuaded I become that 
whatever * coarse ' affections and passions I have are in 
very truth constituted bys and made up ofs those bodily 
changes which we ordinarily call their expression or con- 
sequence; and the more it seems to me thats if I were to 
become corporeally anaesthetics I should be excluded from 
the life of the affectionSs harsh and tender alikcs and drag 
out an existence of merely cognitive or intellectual form." 





II. Extract from a lecture by A. H. Fison on " The 
Evolution of Double Stars " in Lectures on the 
Method of Science, Edited by T. B. Strong: 

The leading points of Darwin's ^^ investigations of the 

12 Professor George Darwin. 



DOUBLE STARS 285 

past history of the moon: " From the fact that the intensity 
of the moon's attraction is greater upon the parts of the 
Earth that are nearer to it than upon the parts that are 
more remote there arises a tendency for the earth to be- 
come stretched along the diameter that is at that particular 
instant directed towards the Moon. If the Earth were 
fluids it would yield to this tendency, but, as it is in the 
main solid, it is unable to do so. The waters upon its 
surface are, however, free, and they consequently flow, con- 
tinually tending to accumulate in two high tides, one im- 
mediately under the Moon, and the other at the part of the 
Earth's surface that is most remote from it. If the period 
of the Earth's rotation was the same as that of the Moon's 
revolution round it, the Moon would continually face the 
same regions of the Earth, and in the course of time, pos- 
sibly a few months or years, the water would reach a 
position of equilibrium, forming permanent high tides at 
the opposite ends of the diameter that would then be per- 
manently directed to the Moon. 

** This simple condition is, however, profoundly modified 
by the Earth's rotation. As the Earth turns under the 
Moon in a period of slightly less than twenty-flve hours, 
the regions presented to the Moon — those at which the 
water tends to accumulate — are continually changing, and 
before any portion of water could move appreciably to- 
wards them, the forces acting upon it would change it and 
it would be urged in some other direction. The problem 
thus becomes extremely complicated. The general result, 
however, is, that in its continual endeavor to move towards 
the ends of the terrestrial diameter that is at each given 
instant pointing to the Moon, the water on the Earth's 
surface is thrown into the continual motion that we recog- 
nize as tidal ebb and flow. 

"If the movement of the water were unresisted by fric- 
tion, tidal ebb and flow would possess no cosmical signifi- 
cance, but friction is experienced in the motion of the tidal 
wave over the surface of shores and estuaries, and in in- 
ternal motions of the water itself. The destruction of 
motion by friction develops heat, and the Earth is conse- 
quently warmed by its tides; moreover, since heat is a 
form of energy, some other form of energy, equivalent in 



286 TYPICAL SYSTEMS OF KNOWLEDGE 

amount^ must disappear in producing it. From considera- 
tions of a not very difficult nature^ it can be shown that this 
energy is that of the Earth's rotation^ so that we are pre- 
sented with the remarkable fact that the speed of the 
Earth's rotation is being reduced in consequence of the 
tides. The period of the Earth's rotation determines the 
day^ and consequently the day must be increasing in length. 
No doubt the rate of increase is now very slight^ but there 
can be little doubt that this has not always been the case. 
The Earth was at one time a mass of molten rock^ in which 
bodily tides must have been formed^ while friction must 
have been far greater in the case of such a viscous mass 
than in water. Further^ as we shall see^ the Moon must 
have been nearer the Earth than it is now, and its tide- 
producing power consequently more intense. Under these 
conditions we can well imagine that the loss of rotation 
proceeded at a comparatively rapid pace, and that the day 
was formerly far shorter than it is at the present time. 

** The slackening of the Earth's rotation is not, however, 
the only result of tidal friction. A reaction upon the Moon 
is inevitable, and it appears that, as a necessary conse- 
quence, the Moon must recede from the Earth, its orbital 
speed decreasing at the same time. Its period of revolu- 
tion round the Earth, which we may define as the month, 
is therefore increasing, so that in consequence of the tides, 
the day and the month are both becoming longer. It fol- 
lows, however, from simple considerations, that this cannot 
continue indefinitely. The day is increasing, and so also 
is the month, but there must come a time when the day must 
increase more rapidly than the month (already past), and 
it must ultimately overtake it. The length of each will 
then be fifty-five of our present days. The Earth, then 
rotating in the same period as that of the Moon's revolution 
round it, will continually present the same regions to the 
Moon, as the Moon already presents the same face to it. 
At the ends of the terrestrial diameter that will then be 
constantly pointing towards the Moon, permanent high 
tides will accumulate; ebb and flow, and with it tidal fric- 
tion will cease, and a state of stable equilibrium will be 
reached. It is impossible to determine the epoch of this 
stage, but under the most favorable conditions it must be 



DOUBLE STARS 287 

measured by hundreds of millions of years from the present 
time. ... In the past the Earth must have rotated 
more rapidly, the Moon must have been nearer, and it must 
have revolved in a shorter period than at present. From 
the application of mathematics to the problem, Darwin has 
shown that there must have been a time when the Moon 
was quite close to the surface of the Earth, and, when in 
this condition, the further suggestive fact appears that its 
period of revolution, the month, coincided, as it will again 
coincide in the last stage, with that of the Earth's rotation, 
the day. Both must then have been between three and 
five hours in length. In this first, as in the last condition, 
we see Earth and Moon rotating as a whole about their 
common center of mass, each continually presenting the 
same face to each other. While, however, in the first con- 
dition they are nearly in contact and represent a passing 
phase, in the last they are far apart, and their condition 
is permanent. It is possible to show that the first stage 
could not have occurred less than 50,000,000 years ago." 



/ 



III. Huxley's lecture on " The Demonstrative Evidence 
of Evolution " (with a few omissions) : 

" The occurrence of historical facts is said to be demon- 
strated, when the evidence that they happened is of such 
a character as to render the assumption that they did not 
happen in the highest degree improbable; and the question 
I now have to deal with is, whether evidence in favor of 
the evolution of animals of this degree of cogency is, or is 
not, obtainable from the record of the succession of living 
forms which is presented to us by fossil remains. 

'' Those who have attended to the progress of palaeon- 
tology are aware that evidence of the character which I 
have defined has been produced in considerable and con- 
tinually increasing quantity during the last few years. In- 
deed, the amount and the satisfactory nature of that 
evidence are somewhat surprising, when we consider the 
conditions under which alone we can hope to obtain it. 

" It is obviously useless to seek for such evidence, except 
in localities in which the physical conditions have been 



288 TYPICAL SYSTEMS OF KNOWLEDGE 

such as to permit of the deposit of an unbroken^ or but 
rarely interrupted^ series of strata through a long period 
of time; in which the group of animals to be investigated 
has existed in such abundance as to furnish the requisite 
supply of remains; and in which^ finally^ the materials 
composing the strata are such as to insure the preservation 
of these remains in a tolerably perfect and undisturbed 
state. 

** It so happens that the case which^ at present^ most 
nearly fulfills all these conditions is that of the series of 
extinct animals which culminates in the Horses; by which 
term I mean to denote not merely the domestic animals 
with which we are so well acquainted^ but their allies^ the 
ass^ zebra^ quagga^ and the like. In shorty I use ' horses ' 
as the equivalent of the technical term Equidoe, which is 
applied to the whole group of existing equine animals. 

" The horse is in many ways a remarkable animal ; not 
least so in the fact that it presents us with an example of 
one of the most perfect pieces of machinery in the living 
world. In truth^ among the works of human ingenuity it 
cannot be said that there is any locomotive so perfectly 
adapted to its purposes, doing so much work with so small 
a quantity of fuel, as this machine of nature's manufacture 
— the horse. . . . Look at the perfect balance of his 
form, and the rhythm and force of its action. The loco- 
motive machinery is, as you are aware, resident in its 
slender fore and hind limbs; they are flexible and elastic 
levers, capable of being moved by very powerful muscles; 
and, in order to supply the engines which work these levers 
with the force which they expend, the horse is provided with 
a very perfect apparatus for grinding its food and extract- 
ing therefrom the requisite fuel. 

" Without attempting to take you very far into the 
region of osteological detail, I must nevertheless trouble 
you with some statements respecting the anatomical struc- 
ture of the horse; and, more especially, will it be needful 
to obtain a general conception of the structure of its fore 
and hind limbs, and of its teeth. But I shall only touch 
upon those points which are absolutely essential to our 
inquiry. 

" Let us turn in the first place to the fore-limb. In 



HUXLEY ON EVOLUTION 289 

most quadrupeds^ as in ourselves^ the fore-arm contains 
distinct bones^ called the radius and the ulna. The cor- 
responding region in the horse seems at first to possess but 
one bone. Careful observation, however, enables us to 
distinguish in this bone a part which clearly answers to the 
upper end of the ulna. This is closely united with the chief 
mass of the bone which represents the radius, and runs 
out into a slender shaft which may be traced for some dis- 
tance downwards upon the back of the radius, and then in 
most cases thins out and vanishes. It takes still more 
trouble to make sure of what is nevertheless the fact, that 
a small part of the lower end of the bone of a horse's fore- 
arm, which is only distinct in a very young foal, is really 
the lower extremity of the ulna. 

*' What is commonly called the knee of a horse is its 
wrist. The ' cannon bone ' answ^ers to the middle bone 
of the five metacarpal bones, which support the palm of 
the hand in ourselves. The * pastern,' ' coronary,' and 
'coffin' bones of veterinarians answer to the joints of our 
middle fingers, while the hoof is simply a greatly enlarged 
and thickened nail. But if what lies below the horse's 
' knee ' thus corresponds to the middle finger in ourselves, 
what has become of the four other fingers or digits ? We 
find in the places of the second and fourth digits only two 
slender, splint-like bones, about two-thirds as long as the 
cannon bone, which gradually taper to the lower ends and 
bear no finger joints, or as they are termed, phalanges. 
Sometimes, small bony or gristly nodules are to be found 
at the bases of these two metacarpal splints, and it is prob- 
able that these represent rudiments of the first and fifth 
toes. Thus the part of the horse's skeleton which cor- 
responds w^ith that of the human hand contains one over- 
grown middle digit, and at least two imperfect lateral 
digits; and these answer, respectively, to the third, the 
second, and the fourth fingers in man. 

" Corresponding modifications are found in the hind 
limb. In ourselves, and in most quadrupeds, the leg con- 
tains two distinct bones — a large bone, the tibia, and a 
smaller and more slender bone, the fibular. But, in the 
horse, the fibular seems, at first, to be reduced to its upper 
end ; a short, slender bone, united with the tibia and ending 



290 TYPICAL SYSTEMS OF KNOWLEDGE 

in a point below^ occupying its place. Examination of the 
lower end of a young foal's shin-bone^ however^ shows a 
distinct portion of osseous matter which is the lower end of 
the fibula; so that the apparently single lower end of the 
shin-bone is really made up of the coalesced ends of the 
tibia and fibula^ just as the apparently single lower end 
of the fore-arm bone is composed of the coalesced radius 
and ulna. 

*' The heel of the horse is the part commonly known as 
the hock. The hinder cannon bone answers to the middle 
metatarsal bone of the human foot; the pastern^ coronary^ 
and coffin bones^ to the middle toe bones; the hind hoof to 
the nail; as in the fore-foot. And^ as in the fore-foot^ 
there are merely two splints to represent the second and 
the fourth toes. Sometimes a rudiment of the fifth toe 
appears to be traceable. 

** The teeth of the horse are not less peculiar than its 
limbs. The living engine^ like all others^ must be well stoked 
if it is to do its work; and the horse, if it is to make 
good its wear and tear^ and to exert the enormous amount 
of force required for its propulsion^ must be well and 
rapidly fed. To this end^ good cutting instruments and 
powerful and lasting crushers are needful. Accordingly^ 
the twelve cutting teeth of a horse are close-set and con- 
centrated in the fore part of its mouthy like so many adzes 
or chisels. The grinders or molars are large^ and have 
an extremely complicated structure^ being composed of a 
number of different substances of unequal hardness. The 
consequence of this is that they wear away at different 
rates; and^ hence^ the surface of each grinder is always as 
uneven as that of a good mill-stone. 

" I have said that the structure of the grinding teeth is 
very complicated^ the harder and the softer parts beings 
as it were^ interlaced with one another. The result of this 
is that^ as the tooth wears^ the crown presents a peculiar 
pattern^ the nature of which is not very easily deciphered at 
firsts but which it is important that we should understand 
clearly. Each grinding tooth of the upper jaw has an 
outer wall so shaped that^ on the worn crown^ it exhibits 
the form of two crescents^ one in front and one behind^ 
with their concave sides turned outwards. From the inner 



HUXLEY ON EVOLUTION 291 

sides of the front crescent^ a crescentic front ridge passes 
inwards and backwards^ and its inner face enlarges into a 
strong logitudinal fold or pillar. From the front part of 
the hinder crescent_, a hack-ridge takes a like- direction^ and 
also has its pillar, 

" The deep interspaces or valleys between these ridges 
and the outer wall are filled by bony substance^ which is 
called cement, and coats the whole tooth. 

** The pattern of the worn face of each grinding tooth of 
the lower jaw is quite diiferent. It appears to be formed 
of two crescent-shaped ridges^ the convexities of which are 
turned outwards. The free extremity of each crescent has 
a pillar, and there is a large double pillar where the two 
crescents meet. The whole structure is^ as it were^ em- 
bedded in cement^ which fills up the valleys^ as in the 
upper grinders. 

*' If the grinding faces of an upper and of a lower 
molar are applied together^ it will be seen that the opposed 
ridges are nowhere parallel^ but that they frequently cross ; 
and that thus^ in the act of mastication^ a hard surface 
in the one is constantly applied to a soft surface in the 
other and vice versa. They thus constitute a grinding ap- 
paratus of great efficiency^ and one which is repaired as fast 
as it wears^ owing to the long continued growth of the 
teeth. 

*' Some other peculiarities of the dentition of the horse 
must be noticed^ as they bear upon what I shall have to 
say by-and-by. Thus^ the crowns of the cutting teeth 
have a peculiar deep pit^ which gives rise to the well-known 
' mark ' of the horse. There is a large space between the 
outer incisors and the front grinder. In this space the 
adult male horse presents, near the incisors, one on each 
side, above and below, a canine or ' tush,' which is com- 
monly absent in mares. In a young horse, moreover, there 
is not infrequently to be seen, in front of the first grinder, 
a very small tooth, which soon falls out. If this small tooth 
be counted as one, it will be found that there are seven 
teeth behind the canine on each side, namely, the small 
tooth in question, angd six great grinders, among which, by 
an unusual peculiarity, the foremost tooth is rather larger 
than those which follow it. 



292 TYPICAL SYSTEMS OF KNOWLEDGE 

" I have now enumerated those characteristic structures 
of the horse which are of most importance for the pur- 
pose we have in view. 

** To any one who is acquainted with the morphology of 
vertebrated animals^ they show that the horse deviates 
widely from the general structure of mammals; and that 
the horse type is^ in many respects^ an extreme modifica- 
tion of the general mammalian plan. The least modified 
mammals^ in fact^ have the radius and ulna^ the tibia and 
fibula^ distinct and separate. They have five distinct and 
complete digits on each foot^ and no one of these digits 
is very much larger than the rest. Moreover^ in the least 
modified mammals^ the total number of the teeth is very 
generally forty-four^ while in horses the usual number is 
forty^ and in the absence of the canines it may be reduced 
to thirty-six; the incisor teeth are devoid of the fold seen 
in those of the horse; the grinders regularly diminish in 
size from the middle of the series to its front end; while 
their crowns are shorty early attain their full lengthy and 
exhibit simple ridges or tubercles^ in place of the complex 
foldings of the horse's grinders. 

'' Hence^ the general principles of the hypothesis of evo- 
lution lead to the conclusion that the horse must have been 
derived from some quadruped which possessed fiw^ com- 
plete digits on each foot; which had the bones of the fore- 
arm and of the leg complete and separate; and which 
possessed forty-four teeth^ among which the crowns of the 
incisors and grinders had a simple structure^ while the lat- 
ter gradually increased in size from before backwards^ at 
any rate in the anterior part of the series^ and had short 
crowns. 

'' And if the horse has been thus evolved^ and the remains 
of the different stages of its evolution have been preserved^ 
they ought to present us with a series of forms in which the 
number of the digits becomes reduced; the bones of the 
fore-arm and leg gradually take on the equine condition; 
and the form and arrangement of the teeth successively 
approximate to those which obtain in existing horses. 

'' Let us turn to the facts and see how far they fulfil 
these requirements of the doctrine of evolution. 

" In Europe abundant remains of horses are found in 



HUXLEY ON EVOLUTION 293 

the Quaternary and later Tertiary strata as far as the 
Pliocene formation. But these horses^ which are so com- 
mon in the cave deposits and in the gravels of Europe, 
are in all essential respects like existing horses. And that 
is true of all the horses of the latter part of the Pliocene 
epoch. But in deposits which belong to the earlier Plio- 
cene and later Miocene epochs^ and which occur in Britain^ 
in France^ in Germany^ in Greece^ in India^ we find ani- 
mals which are extremely like horses — which^ in fact^ are 
so similar to horses^ that you may follow descriptions given 
in works upon the anatomy of the horse upon the skeletons 
of these animals — but which differ in some important par- 
ticulars. For example^ the structure of their fore and hind 
limbs is somewhat different. The bones which^ in the 
horse^ are represented by two splints^ imperfect below^ are 
as long as the metacarpal and metatarsal bones; and at- 
tached to the extremity of each is a digit with three joints 
of the same general character as those of the middle digits 
only very much smaller. These small digits are so disposed 
that they could have had but very little functional impor- 
tance^ and they must have been rather of the nature of 
the dew-claws^ such as are to be found in many animals. 
The Hipparion, as the extinct European three-toed horse 
is called^ in fact, presents a foot similar to that of the 
American Protophippus (Fig. 12), except that, in the Ilip- 
parion, the smaller digits are situated further back, and 
are of smaller proportional size, than in the Protohippus. 

" The ulna is slightly more distinct than in the horse; 
and the whole length of it, as a very slender shaft, inti- 
mately united with the radius, is completely traceable. The 
fibula appears to be in the same condition as in the horse. 
The teeth of the Hipparion are essentially similar to those 
of the horse, but the pattern of the grinders is in some 
respects a little more complex, and there is a depression 
on the face of the skull in front of the orbit which is not 
seen in existing horses. 

" In the earlier Miocene and perhaps the later Eocene 
deposits of some parts of Europe, another extinct animal 
has been discovered, which Cuvier, who first described 
some fragments of it, considered to be a Palceotherium, 
But as further discoveries threw no light upon its struc- 



294 TYPICAL SYSTEMS OF KNOWLEDGE 

ture^ it was recognized as a distinct genus, under the name 
of Anchitherium, 

" In its general characters, the skeleton of Anchitherium 
is very similar to that of the horse. In fact, Lartet and 
De Blainville called it P aloe other turn equinum or hippoides; 
and De Christol, in 1847, said that it differed from Hip- 
parion in little more than the characters of its teeth^ and 
gave it the name of Hipparitherium, Each foot possesses 
three complete toes; while the lateral toes are much larger 
in proportion to the middle toe than in Hipparion, and 
doubtless rested on the ground in ordinary locomotion. 

*' The ulna is complete and quite distinct from the 
radius, though firmly united with the latter. The fibula 
seems also to have been complete. Its lower end, though 
intimately united with that of the tibia, is clearly marked 
off from the latter bone. 

" There are forty-four teeth. The incisors have no 
strong pit. The canines seem to be well developed in both 
sexes. The first of the seven grinders, which, as I have 
said, is frequently absent, and, when it does exist, is small 
in the horse, is a good-sized and permanent tooth, while 
the grinder which follows it is but little larger than the 
hinder one. The crowns of the grinders are short, and 
though the fundamental pattern of the horse-tooth is dis- 
cernible, the front and back ridges are less curved, the 
accessory pillars are wanting, and the valleys, much shal- 
lower, are not filled up with cemerit. 

" Seven years ago, when I happened to be looking criti- 
cally into the bearing of palaeontological facts upon the 
(doctrine of evolution, it appeared to me that the Anchithe- 
rium, the Hipparion, and the modern horse constitute a 
series in which the modifications of structure coincide with 
the order of chronological occurrence, in the manner in 
which they must coincide if the modern horses really are 
the result of a gradual metamorphosis, in the course of the 
Tertiary epoch, of a less specialized ancestral form. And 
I found by correspondence with the late eminent French 
anatomist and paleontologist, M. Lartet, that he had arrived 
at the same conclusion from the same data. 

" That the Anchitherium type had become metamor- 
phosed into the Hipparion type, and the latter into the 
Equine type, in the course of that period of time which 



HUXLEY ON EVOLUTION 295 

is represented by the latter half of the Tertiary deposits^ 
seemed to me to be the only explanation of the facts for 
which there was even a shadow of probability. 

" And^ hence^ I have ever since held that these facts 
aiford evidence of the occurrence of evolution^ which^ in 
the sense already defined^ may be termed demonstrative. 

*' All who have occupied themselves with the structure 
of Anchitherium, from Cuvier onwards^ have acknowledged 
its many points of likeness to a well-known genus of ex- 
tinct Eocene mammals^ P alw other ium. Indeed^ as we have 
seen^ Cuvier regarded his remains of Anchitherium as those 
of a species of Palceotherium, Hence^ in attempting to 
trace the pedigree of the horse beyond the Miocene epoch 
and the Anchitheroid form^ I naturally sought among the 
various species of Palseotheroid animals for its nearest 
ally^ and I was led to conclude that the Palceotherium minus 
(Plagiolophus) represented the next step more nearly than 
any other form then known. 

" I think that this opinion was fully justifiable; but the 
progress of investigation has thrown an unexpected light 
on the question^ and has brought us much nearer than could 
have been anticipated to a knowledge of the true series of 
the progenitors of the horse. 

*' You are all aware that when your country was first 
discovered by Europeans^ there were no traces of the ex- 
istence of the horse in any part of the American continent. 
The accounts of the conquest of Mexico dwell upon the 
astonishment of the natives of that country when they first 
became acquainted with that astounding phenomenon — a 
man seated upon a horse. Nevertheless^ the investigations 
of American geologists have proved that the remains of 
horses occur in the most superficial deposits of both North 
and South America^ just as they do in Europe. Therefore^ 
for some reason or other^ — no feasible suggestion on that 
subject^ so far as I know^ has been made^ — the horse must 
have died out in this continent at some period preceding 
the discovery of America. Of late years there has been 
discovered in your Western Territories that marvellous ac- 
cumulation of deposits^ admirably adapted for the preser- 
vation of organic remains^ to which I referred the other 
evenings and which furnishes us with a consecutive series 
of records of the fauna of the older half of the Tertiary 



296 TYPICAL SYSTEMS OF KNOWLEDGE 



epoch^ for which we have no parallel in Europe. They 
have yielded fossils in an excellent state of conservation 
and in unexampled number and variety. The researches 



JIKCKNT. 

£QUUS. 



l>LIOCENE. 

PLIOHIPPUS. 



PROTOHLPPUS 

(Hipparion). 



MIOCENE;. 

MIOHIPPUS. 

(Anchilherium). 



MESOHIPPUS. 



Fore Hind Eore Lower 

Foot. Foot. Arm. I^eg-. Upper Molar. Molar. 




EOCENE. 



OROHIPPUS. 




Fig. 12. 

of Leidy and others have shown that forms allied to the 
Hipparion and the Anchitherium are to be found among 



HUXLEY ON EVOLUTION 297 

these remains. And it is only recently that the admirably 
conceived and most thoroughly and patiently worked-out 
investigations of Professor Marsh have given us a just idea 
of the vast fossil wealth and of the scientific importance 
of these deposits. I have had the advantage of glancing 
over the collections in Yale Museum^ and I can truly say 
that^ so far as my knowledge extends^ there is no collection 
from any one region and series of strata comparable for 
extent^ or for the care with which the remains have been 
got together^ or for their scientific importance^ to the series 
of fossils which he has deposited there. This vast collec- 
tion has yielded evidence bearing upon the pedigree of the 
horse of the most striking character. It tends to show 
that we must look to America^ rather than to Europe^ for 
the original seat of the equine series ; and that the archaic 
forms and successive modifications of the horse's ancestry 
are far better preserved here than in Europe. 

" Professor Marsh's kindness has enabled me to put be- 
fore you a diagram^ every figure in which is an actual repre- 
sentation of some specimen which is to be seen at Yale 
at this present time (Fig. 12). 

" The succession of forms which he has brought together 
carries us from the top to the bottom of the Tertiaries. 
Firstly^ there is the true horse. Next we have the American 
Pliocene form of the horse (Pliohippus) ; in the conforma- 
tion of its limbs it presents some very slight deviations 
from the ordinary horse^ and the crowns of the grinding 
teeth are shorter. Then comes the Protohippus, which 
represents the European Hipparion, having one large digit 
and two small ones on each foot^ and the general charac- 
ter of the fore-arm and leg to which I have referred. But 
it is more valuable than the European Hipparion for the 
reason that it is devoid of some of the peculiarities of that 
form — peculiarities which tend to show that the European 
Hipparion is rather a member of a collateral branch than 
a form in the direct line of succession. Next, in the back- 
ward order in time, is the Miohippus, which corresponds 
pretty nearly with the Anchitherium of Europe. It pre- 
sents three complete toes — one large median and two smal- 
ler lateral ones ; and there is a rudiment of that digit which 
answers to the little finger of the human hand. 

*' The European record of the pedigree of the horse 



298 TYPICAL SYSTEMS OF KNOWLEDGE 

stops here; in the American Tertiaries^ on the contrary^ 
the series of ancestral equine forms is continued into the 
Eocene formations. An older Miocene form^ termed Meso- 
hippuSy has three toes in fronts with a large splint-like 
rudiment representing the little finger^ and three toes be- 
hind. The radius and the ulna^ the tibia and the fibula^ 
are distinct^ and the short-crowned molar teeth are Anchi- 
theroid in pattern. 

" But the most important discovery of all is the Oro- 
hippuSy which comes from the Eocene formation^ and is the 
oldest member of the equine series^ as yet known. Here 
we find four complete toes on the front limb^ three toes 
on the hind limb^ a well-developed ulna^ a well-developed 
fibula^ and short-crowned grinders of simple pattern. 

*' Thus^ thanks to these important researches^ it has be- 
come evident that^ so far as our present knowledge ex- 
tends^ the history of the horse-type is exactly that which 
could have been predicted from a knowledge of the prin- 
ciples of evolution. And the knowledge we now possess 
justifies us completely in the anticipation that when the 
still lower Eocene deposits^ and those which belong to the 
Cretaceous epoch^ have yielded up their remains of ances- 
tral equine animals^ we shall find^ first^ a form with four 
complete toes and a rudiment of the innermost first digit 
in fronts with probably^ a rudiment of the fifth digit in 
the hind foot;^^ while^ in still older forms^ the series of 
digits will be more and more complete^ until we come to the 
five-toed animals^ in which^ if the doctrine of evolution is 
^ well-founded^ the whole series must have taken its origin. 

" This is what I mean by the demonstrative evidence 
of evolution. An inductive hypothesis is said to be demon- 
strated when the facts are shown to be in entire accordance 
with it. If that is not scientific proof ^ there are no merely 
inductive conclusions which can be said to be proved. And 
the doctrine of evolution^ at the present time^ rests upon 
exactly as secure a foundation as the Copernican theory 
of the motions of the heavenly bodies did at the time of its 
promulgation. Its logical basis is precisely of the same 
character — the coincidence of the observed facts with theo- 
retical requirements. 

13 Remains of animals corresponding very closely to this de- 
scription were afterwards discovered. 



HUXLEY ON EVOLUTION 299 

" The only way of escape^ if it be a way of escape^ from 
the conclusions which I have just indicated, is the suppo- 
sition that all these different equine forms have been 
created separately at separate epochs of time; and, I re- 
peat^ that of such an hypothesis as this there neither is, 
nor can be, any scientific evidence; and assuredly, so far 
as I know, there is none which is supported, or pretends 
to be supported, by evidence or authority of any other 
kind. I can but think that the time will come when such 
suggestions as these, such obvious attempts to escape the 
force of demonstration, will be put upon the same footing 
as the supposition made by some writers, who are, I be- 
lieve, not completely extinct at present, that fossils are 
mere simulacra, are no indications of the former existence 
of the animals to which they seem to belong; but that they 
are either sports of Nature, or special creations. . . 

'* In fact, the whole evidence is in favor of evolution, and 
there is none against it. And I say this, although perfectly 
well aware of the seeming difficulties which have been 
built up upon what appears to the uninformed to be a 
solid foundation. I meet constantly with the argument 
that the doctrine of evolution cannot be well founded, be- 
cause it requires the lapse of a very vast period of time; 
while the duration of life upon the earth, thus implied, is 
inconsistent with the conclusions arrived at by the as- 
tronomer and the physicist. I may venture to say that I 
am familiar with those conclusions, inasmuch as some years 
ago, when President of the Geological Society of London, 
I took the liberty of criticising them, and of showing in 
what respects, as it appeared to me, they lacked complete 
and thorough demonstration. But, putting that point aside, 
suppose that, as the astronomers, or some of them, and 
some physical philosophers, tell us, it is impossible that life 
could have endured upon the earth for as long a period 
as is required by the doctrine of evolution — supposing that 
to be proved — I desire to be informed what is the founda- 
tion for the statement that evolution does require so great 
a time. The biologist knows nothing whatever of the 
amount of time which may be required for the process of 
evolution. It is a matter of fact that the equine forms, 
which I have described to you, occur in the order stated in 
the Tertiary formations. But I have not the slightest 



300 TYPICAL SYSTEMS OF KNOWLEDGE 

means of guessing whether it took a million of years^ or 
ten millions^ or a hundred millions^ or a thousand millions 
of years^ to give rise to that series of change. 

" A biologist has no means of arriving at any conclusion 
as to the amount of time which may be needed for a certain 
quantity of organic change. He takes his time from the 
geologist. The geologist^ considering the rate at which de- 
posits are formed and the rate at which denudation goes 
on upon the surface of the earthy arrives at more or less 
justifiable conclusions as to the time required for the de- 
posit of a certain thickness of rocks; and if he tells me 
that the Tertiary formations required 500^000^000 years 
for their deposit^ I suppose he has good ground for what 
he says^ and I take that as a measure of the duration of 
the evolution of the horse from the Orohippus up to its 
present condition. And^ if he is rights undoubtedly evolu- 
tion is a very slow process^ and requires a great deal of 
time. But suppose^ now^ that an astronomer or a physicist 
— for instance^ my friend^ Sir William Thomson — tells me 
that my geological authority is quite wrong; and that he 
has weighty evidence to show that life could not possibly 
have existed upon the surface of the earth 500^000^000 
years ago^ because the earth would have then been too hot 
to allow of lif e^ my reply is : * That is not my affair ; set- 
tle that with the geologist^ and when you have come to an 
agreement among yourselves^ I will adopt your conclu- 
sion.' We take our time from the geologists and physicists ; 
and it is monstrous that^ having taken our time from the 
physical philosopher's clock_, the physical philosopher should 
turn round upon us^ and say we are too fast or too slow. 
What we desire to know is^ is it a fact that evolution took 
place? As to the amount of time which evolution may have 
occupied, we are in the hands of the physicists and as- 
tronomers_, whose business it is to deal with those questions." 



INDEX 



Abstractions, 45 

Abstract terms, 54 

Aikins, 163, 205 

Amphibology, 73 

Analogy, 251; rules of, 252 

Analysis, 46, 88 

Antecedent probability, 277 

Astronomy, 265 

Average deviation, 206 

Average, deviation from, 205 

Average error, 206 

Averages, 195, 198; arithmet- 
ical, 198; geometrical, 204; 
the median, 202; the mode, 
201 ; " weighted " averages, 
199 

Bain, 104, 271 

Baldwin, 11, 238 

Biology, 35, 42, 208, 262 

Bosanuqet, 34 

Bowley, 192, 194, 200, 202, 203, 

204, 207, 229, 230. 
Burnet, 249 

Causal law, 81, 82 
Cause, 81 
Chamberlain, 250 
Chemistry, 262 
Circumstantial evidence, 279 
Collective judgments, 86 
Collective terms, 56 
Collusion, 276 
Composition of causes, 97, 193 



Classification, 6, 32, 49, 79, 195; 
artificial, 33; diagnostic, 33; 
index, 32; natural, 33; req- 
uisites of, 40, 49 

Common sense, 1 

Comparison of quantities, 210 

Composition, fallacy of, 57 

Concept, conception, 45 

Concrete terms, 54 

Contradictory propositions, 114 

Contraposition, 122 

Contrary propositions, 114 

Conversion, 119 

Correlation, 191 

Counteracting causes, 97, 193 

Cramer, 248, 250 

Cross-division, 41 

Curves, 226 

Cuvier, 12 

Darwin, 248, 249 

Deduction, 110; a part of 

scientific method, 2 
Definition, 57; defects of, 60 
DeMorgan, 77 
Deviations from an averagCj 

205 
Dilemma, The, 159 
Discrimination, 45 
Disjunctive reasoning, 157 
Distributive terms, 56 
Distribution of terms, 71 
Division, 37; dichotomous, 38; 

incomplete, 40; rules of, 40; 

fallacy of, 56 



301 



302 



INDEX 



Documents, 266 

Elimination in the inductive 
methods, 96 

Enthymeme, 151 

Enumeration, complete, 84; in- 
complete or simple, 83, 190 

Error, 206; curve of, 231 

Errors, three kinds, 18; causes 
of, 19 

Euclid, 25S 

Euler's Method, 72, 120 

Evidence, 48 ; circumstantial, 
279; external, 270; hearsay, 
278; indirect, 278; internal, 
270 

Exceptive propositions, 76 

Exclusive propositions, 75 

Experiment, 24 

Explanation, 237; general, 240; 
specific, 240, 244 

External evidence, 270 

Extra-syllogistic reasoning, 162 

Fallacies, formal, 138, 173; of 
accent, 76; of amphibology, 
73; of assumption, 171; of 
converse accident, 55; of 
composition, 57; of division, 
57; of figure of speech, 76; 
of four terms, 138; of hypo- 
thetical reasonings 157; of 

'illicit major, 141; of illicit 
minor, 141; of missing the 
point, 171 ; of non-sequitur, 
174; of perception, 16; of 
petitio principii, 172; of post 
hoc ergo propter hoc, 174; of 
undistributed middle, 138 

Figures of the syllogism, 126, 
142; principles of, 126; rules 
for, 126 



Fison, 284 

Fowler, 90 

Fundannentun dimsionis, 34, 41 

Facts, 13 

Galton, 203 
Generalization, 79 
General terms, 52 
Genus, 41 
Geology, 264 
Geometry, 258 
Gomperz, 255 
Graphic method, 266 

Hadley, 249 

Hayward, 276 

Hearsay evidence, 278 

Helmholz, 208 

Hibben, 111, 123 

History, 264 

Hobhouse, 240, 253 

Huxley, 1, 12, 36, 248, 278 

Hypotheses, 246; value of, 
246; value of erroneous, 249; 
how suggested, 251 ; requi- 
sites of, 253 

Hypothetical reasoning, 157; 
rules of, 157 

Hyslop, 38, 73, 75, 120 

Induction, 2, 79; perfect, 85; 
mathematical, 168 

Inductive inference, €1 

Inductive methods, 88; agree- 
ment, 90; difference, 95; the 
joint method, 98; concomi- 
tant variations, 102; residues, 
104 

Inference, 6, 14, 15, 29 

Infima species, 42 

Internal evidence, 270 



INDEX 



303 



James, 21, 113, 208, 263, 280; 

theory of the emotions, 280 
Jevons, 33, 36, 76, 150, 209, 219, 

221, 239 
Joseph, 69 

Kant, 4, 9 

Knowledge, the beginning of, 
3; the sources of, 5; organ- 
izing, 6 

Langlois and Seignobos, 250, 

266, 269, 279 
Language, 7, 48 
Law, 79, 237; how discovered, 

8, 189 
Laws of thought, 1, 10 
Linnaeus, 34 
Locke, 4, 9, 76 
Lotze, 223 

Material facts, 266 

Mayo-Smith, 196 

Meaning, 47 

Measurement, 208 

Mechanics, 262 

Median, 202 

Median error, 206 

Memory, 5, 26, 48 

Mendel's Law, 263 

Methods, inductive, 88 

Mill, 84, 86, 91, 95, 96, 101, 102, 

105 
Minto, 251, 255 
Mode, the, 201 

Moods of the syllogism, 140 
Muirhead, 245 

Natural classifications, 33 
Natural science, 4, 12 
Negative evidence, 276 
Newton, 247 



Observation, 18, 48, 79, 88; 

mistakes of, 18 
Obversion, 121 

Opposition of propositions, 114 
Order, 42 

Pearson, 32, 192, 208 

Perception, 5^ 13; "fallacies" 
of, 16; how tested, 23 

Predicables, 60 

Predicate, 68 

Plurality of causes, 94, 193 

Porphyry, 37 

Premises, 126 

Presuppositions of knowledge, 
9 

Proof, 166; direct, 166; indi- 
rect, 166; in geometry, 168 

Probability, 213; curve of, 231; 
deduction of, 216; dangers in 
interpreting, 223 

Probable error, 206 

Propositions, 66; quantity and 
quality of, 66; and terms, 
68; ambiguous, 73; exceptive, 
76; exclusive 75 

Pro-syllogism and epi-syllo- 
gism, 152 

Psychology, 262 

Punnett, 253 

Reduction of the moods and 

figures, 158 
Romanes, 247 
Russell, 59 

Scientific law, 8 

Science' and common sense, 1 

Science, 259 

Scott, 264 

Sedgwick and Wilson, 35 



304 



INDEX 



Seignobos, Langlois and, 250, 
266, 269, 279 

Self-evident propositions, 79 

Sigwart, 196, ^43, 251 

Singular terms, 52 

Sorites, 155 

Species, 41 

Spencer, 61 

Statistics, 189; collection of, 
193, 194; tabulation, 194; 
summary, 194; critical exam- 
ination of, 194; often un- 
necessary, 195; often inappli- 
cable, 196 

Subalterns, 114 

Subcontraries, 114 

Subject, 68; grammatical, 68; 
logical, 68; metaphysical or 
ultimate, 69 

Sui generis, 42 

Summun genus, 41 

Syllogism, 111; criticism of, 
111; principles of, 126; rules 
of, 137 

Symbols, 47 



Systematic knowledge. 111 

Terms, 49; distribution of, 71; 
generalization of, 50; spe- 
cialization of, 50; transfer of 
meaning of, 51; kinds of, 52; 
and propositions, 68 

Testimony, 6, 28, 266; sources 
of error in, 28 

Testing inductive inference, 83, 
89 

Testing perceptions, 23 

Thorndike, 192, 211, 234, 263 

Tradition, 278 

Variety, 42 
Veblen, 258 

Verification, 8, 81, 86, 110 
Voltaire, 274 

Washburn, 253 
Witness, The, 269 
Wilson, Sedgwick and, 35 

Yerkes, 263 
Young, 197 



4 



Hmerican Science Series 

The two principal objects of the series are to supply author- 
itative books whose principles are, so far as practicable, illus- 
trated by American facts, and also to supply the lack that 
the advance of science perennially creates, of text-books 
which at least do not contradict the latest generalizations. 

Physics. 

By A. L. KiMBAivi^, Professor in Amherst College. {In 
preparation.) 

Physics. 

By Georgia F. Barker. x-f902 pp. $3.50. 

Chemistry. 

By Ira Rkmsen, President of the Johns Hopkins Uni- 
versity. 

Advanced Course, xxii + 853 pp. $3.00. 
College Chemistry, xx + 689 pp. $2.25. 
Briefer Course, xxiv + 516 pp. $1.25. 
Elementary Course, x + 287 pp. 80 cents. 

Astronomy. 

By Simon Newcomb and Edward S. H01.DEN. 

Advanced Course, xii + 512 pp. $2.00. 
Briefer Course, x + 366 pp. $1.20. 
Elementary Course, xv + 446 pp. $1.20. 

Geology. 

By Thomas C. Chamberlin and R01.LIN D. Salisbury, 
Professors in the University of Chicago. 3 vols. 8vo. 

Vol. I. Geological Processes and their Results, xix 
+ 654 pp. $4.00. 

Vols. II and III. Earth History, xxxvii + 1316 pp. 
{Not sold separately.) $8.00. 

Physiography. 

By R01.UN D. Sawsbury, Professor in Chicago Univer- 
sity. 

Advanced Course, xx + yyopp. $3.50. 

Briefer Course, viii -|- 5 3 1 pp. $ i . 50. 



^ 



\ 



General Biology. 

By W1LI.1AM T. Shdgwick, Professor in the Mass. Insti= 
tute, and Edmund B. WiIvSON, Professor in Columbia, 
University, xii + 231 pp. $1.75. 

Botany. 

By CharIvEs E. BessEy, Professor in the University of 
Nebraska. 

Advanced Course. x + 6ii pp. $2.20. 
Briefer Course, vii + 356 pp. $1.12. 

Zoology. 

By A. S. Packard. 

Advanced Course. viii4-722 pp. $2.50. 
Briefer Course, viii + 338 pp. $1.12. 
Elementary Course, viii + 290 pp. 80 cents^ 

The Human Body. 

By H. NewEi^Iv Martin. 

Advanced Course, xvi + 685 pp. $2.50. 
Briefer Course, xiv + 408 pp. $1.25. 
Elementary Course, vi + 261 pp. 80 cents. 

Psychology. 

By WiiyiyiAM James, Professor m Harvard University, 

Advanced Course. 2 volumes. $5.00. 
Briefer Course, xiii + 478 pp. $1.60. 

Ethics. 

By John DewEy, Professor in Columbia University, and 
James H. Tufts, Professor in the University of Chicago. 
(Jn press.) 

Political Economy. 

By Francis A. Walker. 

Advanced Course, viii + 537 pp. $2.00. 
Briefer Course, viii+415 pp. $1.20. 
Elementary Course, x + 323 pp. $1.00. 

Finance. 

By Henry C. Adams, Professor in the University of Mich- 
igan. xiv + 573 pp. $3.00. 

HENRY HOLT & CO, 378 Wabash Ave.,^ciiic5^o 






Deacidified using the Bookkeeper process. 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Sept. 2004 

PreservatiofiTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive 
Cranberry Township, PA 16066 
(72_4)_779-2111 



i 



